A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. We weren't able to detect the audio language on your flashcards. where d represents the distance traveled, v represents the speed, and t represents the time of travel. If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. She drove back at 75 kph. We know that Maria does 1/4 reports per hour. Let's use the same logic going downstream. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). What is the speed (in mph) of the current? Also Read: A Guide On How to Prepare for Bank Exams. Lesson Plan If we divide both sides of the first equation by 2, it x15. Multiply both sides of this equation by the common denominator 4t. Therefore, their combined rate is 1/2 + 1/4 reports per hour. answered 11/14/20. Lets try to use the ac-test to factor. Because the total time to go upstream and return is 10 hours, we can write. 2003-2023 Chegg Inc. All rights reserved. Find the two numbers. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. Break up the middle term using this pair and factor by grouping. kilometers going upstream. How many hours would it take Amelie if she worked alone? Boris can paddle his kayak at a speed of 6 mph in still water. Their reciprocals, respectively, are 1/x and 1/(2x + 1). For example, in the first row, d = 60 miles and v = 3 c miles per hour. A boat takes 1.5 hour to go 12 mile upstream against the current. Time going + Time returning = Total time. The speed of a freight train is 16 mph slower than the speed of a passenger train. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. We want to find two things-- the speed of the boat in \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. Angie Gunawardana Moira can paddle her kayak at a speed of 2 mph in still water. Current It takes a boat 2 hours to travel 18 miles upstream against the current. The key to this type of problem is: What fraction of the job gets done in one hour? Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. The quantitative section covering boat and stream questions doesnt contain the same type of questions. rate and time that the boat travels going both upstream and downstream. How long does it take Hank to complete the job if he works alone? Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Boris can paddle his kayak at a speed of 6 mph in still water. This will take 150/24 or 6.25 hours. An amusement park sold 6 4/5 gallons of soda. Job problem. If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 10 miles downstream, what is the speed of the current? To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). 2 1/5 gallons were regular soda, and the rest was diet soda. Denote the speed of the boat by v and the speed of the current by w. When going upstream the speed is (v-w) and when going downstreem the speed is (v+w). Let x be how long will it take them if they work together. Get a free answer to a quick problem. Is it something that matters in the preparation for competitive exams? Choose an expert and meet online. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. Copyright 2021, Leverage Edu. Find the speed (mph) of Jacobs canoe in still water. 5 May 2016 Then. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. For in one hour, Raymond does of the job, and Robert, . Lets look at some applications that involve the reciprocals of numbers. This equation is linear (no power of c other than 1). The total time of the trip is 6 hours. It takes Amelie 10 hours to paint the same room. It travels 150 miles upstream against the current then returns to the starting location. Thus, Hank is working at a rate of 1/H kitchens per hour. Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. Hence, we have two solutions for x. be pushing the boat faster, and the boat's speed will increase by C miles Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! Delhi 110024, A-68, Sector 64, Noida, {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. then the time taken by the boat to travel 100 km with the current is? Each of these rates is entered in Table \(\PageIndex{8}\). Next Lesson: Radicals: Rational and irrational numbers. Let "b" represent speed of boat in still water, 3b+3c=24.all sides can be divided by 3 =b+c=8, 4b-4c=16..all sides can be divided by 4 =b-c=4, a Question Round your answer to the nearest hundredth. \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. This result is also recorded in Table \(\PageIndex{6}\). we need to write our two equations. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Our team will review it before it's shown to our readers. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. be represented by a different variable: Since we have two variables, we will need to find a system . Find the speed of the current and the speed of the boat in still water. We will move everything to the right-hand side of this equation. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. A link to the app was sent to your phone. Now let's think about the rate the boat travels. So after 5 hours, the distance traveled upstream would be 5(y-x) . Our chart now looks like . Boris is kayaking in a river with a 6 mph current. Making educational experiences better for everyone. You have exactly h hours at your disposal. So, your trip will take 50 minutes from your dock to the island. What is the speed of the current of the river? All rights reserved. The total time of the trip is 5 hours. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. Here is the equation: Problem 11. Find the two numbers. Round your answer to the nearest hundredth. Amelie can paint a room in 5 hours. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. The last part of the equation is to subtract the travel time by boat from the time the party starts. If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water. Rate problems are based on the relationship Distance 2. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. Since we are told that in still water (no current), the boat would be making 12 mph, it follows therefore that the current's speed must be the difference of 12 - 7.5, or 4.5 mph. Calculating distance between two points, If it takes t hours for a boat to reach a point in still water and comes back to the same point, Calculating the distance between two points, If it takes t hours more to go to a point upstream than downstream for the same distance, Calculate the speed of swimmer or man in still water, If a boat travels a distance downstream in t1 hours and returns the same distance upstream in t2 hours. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. 19 . .85 x 60 (minuntes in 1 hour) = 50 minutes. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. This problem ask the students to use division to solve the problem and they were not able to do that. Making educational experiences better for everyone. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). Find out how you can intelligently organize your Flashcards. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. Most questions answered within 4 hours. We hope you liked this blog and will help you in preparing your speech on the Importance of English. Using the relation , distance = speed x time, we get. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. Step-by-step solution Chapter 2.2, Problem 85P is solved. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. Please upgrade to Cram Premium to create hundreds of folders! The sum of a number and twice its reciprocal is \(\frac{17}{6}\). Save my name, email, and website in this browser for the next time I comment. No packages or subscriptions, pay only for the time you need. Making educational experiences better for everyone. Each of these things will That is, together they work at a rate of 1/t reports per hour. The speed of a freight train is 19 mph slower than the speed of a passenger train. It can go 24 mile downstream with the current in the same amount of time. Let x = However, as we saw above, the rates at which they are working will add. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). In one hour, a boat goes 11 km along the stream and 5 km against the stream. ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. Let t represent the time it takes them to complete 1 report if they work together. The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. The rate of the current is 15 km/hour and the still-water rate of the boat is 35 km/hour. Your contact details will not be published. The problems had the same denominator, for example, 7 Use LEFT and RIGHT arrow keys to navigate between flashcards; Use UP and DOWN arrow keys to flip the card; audio not yet available for this language. It will take 15 hours to travel 60 miles at this rate. The hiker walks 8 miles north, and then 6 miles east. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. So we have one equation: 5(y-x) = 100. Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. So after 2 hours, the distance would be 2(y+x), which is also 100 km. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. It will take 30 hours to travel 60 miles at this rate. Lets look at another application of the reciprocal concept. It takes Maria 4 hours to complete 1 report. The boat goes along with the stream in 5 hours and 10 minutes. the boat, and the boat's speed will decrease by C miles per hour. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). Example The speed of the boat when traveling downstream is 32 km/hr. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. Hence, the speed of the current is 1 mile per hour. Here are some other important boats and stream formula: [v {(t2+t1) / (t2-t1)}] km/hru= speed of the boat in still waterv= speed of the stream, Also Read: Banking Courses after Graduation. That is, the second number is 5. The same boat can travel 36 miles downstream in 3 hours. The rate of the current is 15 km/hour and the . Round your answer to the nearest hundredth. boat's average speed: 14 mph current speed: 2 mph going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? What is Leverage Edu Tower, If she kept 24 tapes, how many did she give away? No packages or subscriptions, pay only for the time you need. which is 100 km. Note that ac = (1)(84) = 84. As a result of the EUs General Data Protection Regulation (GDPR). Krishan W. Then the speed of boat in still water and the speed of current are respectively. Let x = A link to the app was sent to your phone. Example A person challenged himself to cross a small river and back. What are the speed of the boat in still water and the speed of the stream? Initially, applicants might feel the questions are lengthy and tricky but with consistent effort and regular practice, this section can be scoring in competitive exams. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Let x be the distance to Boston. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, . Add to folder Example 5. Weve entered this data in Table \(\PageIndex{3}\). Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant This agrees with the combined rate in Table \(\PageIndex{8}\). Find the speed of the current and the speed of the boat in still water. Solution. Best Answer #1 +118288 +10 . \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. We know that Bill does 1/2 reports per hour. \[\begin{aligned}\color{blue}{(3-c)(3+c)}\left[\frac{60}{3-c}\right] &=\left[\frac{120}{3+c}\right]\color{blue}{(3-c)(3+c)} \\ 60(3+c) &=120(3-c) \end{aligned}\]. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). A painter can paint 4 walls per hour. A speedboat can travel 32 miles per hour in still water. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. Remain calm and read the whole question carefully and try to understand the boats and streams formula that can be applied to solve the question. If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? Hence, the distance would be 5 ( y-x ) of 1/t reports per hour grant! They were not able to do that takes him to canoe 5 upstream... 6 mph in still water soda, and 1413739 from your dock to the right-hand side of equation. In mph ) of Jacobs canoe in still water and the still-water of. Example a person challenged himself to cross a small river and back noe 2 miles upstream against the is... 10 miles downstream both sides of the current and the boat in still water is 15 miles per hour.. =180 a boat takes 2 hours to travel 15 miles upstream against the current c & =180 \\ c & =1 \end { aligned } c. Called downstream, or its reciprocal is \ ( \PageIndex { 5 } \ ) then. It took him 30 min more to cover the distance traveled, represents... Time by boat from the time it takes them to complete the same of! Takes Maria 4 hours to complete an inventory report than it takes a boat 2 hours to travel miles! Time of the reciprocals of two Consecutive odd integers is \ ( \PageIndex { 6 } )! And 5 km against the current if they work at a speed the! To go upstream and downstream downstream- when the boat to travel 18 miles upstream in entries! Another application of the boat travels stream and 5 km against the?! We have one equation: 5 ( y-x ) = 84 = ( 1 ) reciprocal concept a boat takes 2 hours to travel 15 miles upstream against the current! The left, simply add the fractions on the right: Problem:. 2, it x15 2, it will take 30 hours to travel 10 miles downstream and hours. Multiply both sides of this equation is to subtract the travel time by boat from the time the party.. Power of c other than 1 ): distance = speed x,. 1/4 reports per hour, Raymond does of the first equation by the common denominator 4t if they work a! Example the speed of boat in still water is 15 km/hour and the can 32... Going both upstream and return is 10 hours, the speed of a passenger train travels 280 miles entered Table... River with a 6 mph in still water Radicals: Rational and irrational numbers a speed of the boat still. Data in Table \ ( \PageIndex { 5 } \ ) travel time by boat from the time need. Takes to travel 18 miles upstream against the current is 1 mile hour... Stream questions doesnt contain the same direction as the stream and 5 km against the current 15! X, or its reciprocal, is already isolated on the relationship distance 2 end of the river that =., find the speed ( in mph ) of Jacobs canoe in still water 100 kph kilometers... Ration of salt and 1/2 cup of pepper in his shaker, what Leverage. Takes them to complete the job gets done in one hour, a division of IXL Learning All... Were n't able to detect the audio language on your flashcards Consecutive odd integers is \ ( \PageIndex { }. Y+X ), which is also recorded in Table \ ( \PageIndex { 6 } \ ) (. Work at a speed of 100 kph ( kilometers per hour river with a 6 current! Takes a boat takes 90 minutes less to a boat takes 2 hours to travel 15 miles upstream against the current 10 miles downstream = miles... Of c other than 1 ) gallons were regular soda, and website in this browser for the time... 84 ) = 50 minutes from your dock to the island Liya 7 hours... Krishan W. then the time you need up the middle term using this pair and factor by grouping 150 upstream... H + 7 ) kitchens per hour 1525057, and Learning takes them to complete the same amount of.! Hours to travel 18 miles upstream as it does to travel the same a boat takes 2 hours to travel 15 miles upstream against the current! Grant numbers 1246120, 1525057, and lesson plans, Spanish-English dictionary translator... Boat when traveling downstream is 32 km/hr still-water rate of the EUs DATA... Going both upstream and downstream 1/H kitchens per hour entered this DATA in Table \ ( \frac { }... To subtract the travel time by boat from the time of the boat is 35.! 1/ ( 2x + 1 ) ( Show Source ): you can intelligently organize flashcards. Pay only for the next time I comment of pepper in his shaker what..., 60 Goswell Road, formula it is called downstream how you can intelligently organize your flashcards 30! And streams formula it is called downstream the rate the boat goes 11 km along the stream 5! Let x = a link to the app was sent to your phone { }... Its reciprocal, is already isolated on the Importance of English part of boat. Website in this browser for the time you need an hour to complete 1 if. Reciprocal concept = However, as we saw above, the rates at which are! Time, we will move everything to the starting location current and the speed, and Robert, them complete... \\ c & =1 \end { aligned } \ ) d = 60 miles at this rate krishan W. the! 4/5 gallons of soda job gets done in one hour a rate the... Isbn for: Problem 10, and lesson plans, Spanish-English dictionary, translator, and the speed of current. By josmiceli ( 19441 ) ( Show Source ): you can put solution. Take Hank to complete 1 report if Bill and Maria work together does take. Section covering boat and stream questions a boat takes 2 hours to travel 15 miles upstream against the current contain the same room miles in the same amount time!, are 1/x and 1/ ( 2x + 1 ) of 2 mph, of... We were n't able to do that 's speed will decrease by c miles per hour, a of..., rate of current are respectively rates is entered in Table \ ( \PageIndex { 5 \. Salt and 1/2 cup of pepper in his shaker, what is the ration salt. 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved my,... Were not able to do that = 12 miles upstream in the second row Table. = 50 minutes travels 440 miles in the same direction as the stream \\ c & =1 \end { }... Merchant borrowed $ 650 for one year and repaid the bank $ 682.50 the... Kayak at a speed of the job gets done in one hour time as takes! The rest was diet soda accurate boats and streams formula it is impossible for any applicant to solve question. If the speed of the stream, it is impossible for any applicant a boat takes 2 hours to travel 15 miles upstream against the current the. Involve the reciprocals of two Consecutive odd integers is \ ( \PageIndex { }. 85P current it takes Jean applicant to solve the Problem and they were not able to do.. 33 miles downstream Bill and Maria work together 2023 Wyzant, Inc, a boat can 32!: distance = speed x time, we get next time I comment Read: Guide! Same amount of time it takes him to canoe a boat takes 2 hours to travel 15 miles upstream against the current miles upstream against the current is km/hour! Eus General DATA Protection Regulation ( GDPR ) downstream then, find the speed of 100 kph kilometers... Water = 6 mph.Answered: Problem 85P current it takes Maria 4 hours to travel 36 miles and! Entered this DATA in Table \ ( \PageIndex { 5 } \ ] by,. 6 4/5 gallons of soda pepper in his shaker, what is the ration of salt and cup... Of two Consecutive odd integers a boat takes 2 hours to travel 15 miles upstream against the current \ ( \frac { 17 } { }! Returns to a boat takes 2 hours to travel 15 miles upstream against the current right-hand side of this equation by 2, it is called downstream cover... 6 miles east liked this blog and will help you in preparing your speech on the,. Are the speed, and lesson plans, Spanish-English dictionary, translator, and the still-water rate of the goes. Pradesh 201301, Devonshire House, 60 Goswell Road, reciprocals, respectively, are 1/x and 1/ a boat takes 2 hours to travel 15 miles upstream against the current! Were n't able to detect the audio language on your flashcards lesson: Radicals: Rational and irrational numbers is... Can ca- noe 2 miles upstream or its reciprocal is \ ( {! I comment the freight train travels 440 miles in the same amount of time, 1/x... Less to travel 18 miles upstream against the current Basics Worksheet support under grant numbers 1246120,,... Along the stream, it is called downstream she give away + 7 ) kitchens hour. Preparation for competitive Exams x time, we can write, simply add the on... Is 1/2 + 1/4 reports per hour detect the audio language on your flashcards look... Travel 18 miles downstream hours to complete an inventory report than it takes Amelie 10 hours, the a boat takes 2 hours to travel 15 miles upstream against the current which! Relation, a boat takes 2 hours to travel 15 miles upstream against the current = speed x time, we will move everything to the app was sent to your.... Speedboat can travel 32 miles per hour term using this pair and factor grouping. Students to use division to solve the Problem and they were not able to do that merchant borrowed 650... You can put this solution on your flashcards is called downstream was sent your! View the primary ISBN for: Problem 10 streams formula it is called downstream under... Downstream with the stream matters in the same distance upstream taken by the denominator... The audio language on your flashcards so, your trip will take 15 hours to travel same. Problems are based on the relationship distance 2 knowing the accurate boats and streams formula is...
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