For example, in the first row, d = 60 miles and v = 3 c miles per hour. which is 100 km. Find the speed of the current and the speed of the boat in still water. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. Find out how you can intelligently organize your Flashcards. The above mentioned were the most used and basic boats and stream formulas. Choose an expert and meet online. You have exactly h hours at your disposal. 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. Freshwater, Sydney, NSW 2096, A painter can paint 4 walls per hour. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? or 1/12 of a kitchen per hour. So after 5 hours, the distance traveled upstream would be 5(y-x) . so we have 2 equations which must be solved . .85 x 60 (minuntes in 1 hour) = 50 minutes. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. So we have one equation: 5(y-x) = 100. Rate problems are based on the relationship Distance More answers below Quora User What proportion of the kites are blue? Maria can finish the same report in 4 hours. Carlos can do a certain job in three days, while it takes Alec six days. Find the rate of the current and the rate of the boat in still water. Problem 13. Boris is kayaking in a river with a 6 mph current. How much time will it take to come back? The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Against the same current, it can travel only 16 miles in 4 hours. It takes Amelie 10 hours to paint the same room. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? Find the two numbers. Find the two numbers. Because it takes Liya 7 more hours than it takes Hank, let H + 7 represent the time it takes Liya to paint the kitchen when she works alone. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. What is the probability that the first suggestion drawn will be from the people on the first floor? Besides testing the ability of the student, exams are important. The resulting speed of the boat (traveling upstream) is B-C miles per hour. If Rajiv could make his usual rowing rate twice what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. The total time of the trip is 5 hours. He paddles 5 miles upstream against the current and then returns to the starting location. It will take 15 hours to travel 60 miles at this rate. Job problem. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. We can calculate the rate at which Hank is working alone by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substituting Hanks data from row one of Table \(\PageIndex{7}\). Two people working together can complete a job in six hours. Multiply both sides of this equation by the common denominator 10x(2x + 1). If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? 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. what is the speed of the boat in still water and of the current river? 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, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. Let's see what kinds of equations we can come up with. our information in it: A boat can travel 16 miles up a river in 2 hours. Interest and Loan Concepts That is, \[\text { Work }=\text { Rate } \times \text { Time. Round your answer to the nearest hundredth. If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . Let x = 2 1/5 gallons were regular soda, and the rest was diet soda. On your markGet setMental Math Madness! If they work together, it takes them 8 hours. The sum of a number and its reciprocal is \(\frac{5}{2}\). Get a free answer to a quick problem. The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. x15. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question How long does it take Hank to complete the job if he works alone? We'll choose the easiest equation When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . Here's what the chart looks like before we put any of 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). \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. We know that Maria does 1/4 reports per hour. First, let us explain the meaning of "upstream" and "downstream.". If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. }\], A second important concept is the fact that rates add. Their reciprocals, respectively, are 1/x and 1/(2x + 1). The site owner may have set restrictions that prevent you from accessing the site. Water volume increases 9% when it freezes. In one hour, a boat goes 11 km along the stream and 5 km against the stream. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant Jean can paint a room in 5 hours. This result is also recorded in Table \(\PageIndex{6}\). What was the average speed during the whole journey? Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. This was all about the Boats and streams formula. 2(b + c) = 128. b - c = 32. b . Making educational experiences better for everyone. We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. Here is the guiding principle. Hence, the pair {14/5, 7/2} is also a solution. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. A-258, Bhishma Pitamah Marg, \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. Dont let it confuse you. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. that distance. Moira can paddle her kayak at a speed of 2 mph in still water. Signature Assignment for EDEL 462 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. Going downstream, it can travel 60 miles in the same amount of time. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. How many miles are represented by 6 inches? Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. 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. Distance = Speed Time Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. An amusement park sold 6 4/5 gallons of soda. Sanjay can paint a room in 5 hours. Most questions answered within 4 hours. A link to the app was sent to your phone. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. We'll put this information in our chart: Each row in the chart will give us an equation. Block A, Defence Colony, New Delhi, 2700 = ________________ 4. What is the speed of the boat in still water? Jon P. Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. On the other hand, if x = 2/5, then its reciprocal is 5/2. If we let c represent the speed of the current in the river, then the boats speed upstream (against the current) is 3 c, while the boats speed downstream (with the current) is 3 + c. Lets summarize what we know in a distance-speed-time table (see Table \(\PageIndex{1}\)). be pushing the boat faster, and the boat's speed will increase by C miles 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. How far away was Boston? A hiker follows a trail that goes from camp to lake. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. If we divide both sides of the first equation by 2, it Legal. Then is that fraction of the job that gets done in one hour. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). For in one hour, Raymond does of the job, and Robert, . Junior's boat will go 15 miles per hour in still water. Please sign in to share these flashcards. Let x be how long will it take them if they work together. The speed of the current is miles per hour. The same boat can travel 36 miles downstream in 3 hours. So, let x answer the question. Find the number(s). Solution. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. The sum of a number and its reciprocal is \(\frac{41}{20}\). If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? Find the speed of the current and the speed of the boat in still water. Lets look at some applications that involve the reciprocals of numbers. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). Best Answer #1 +118288 +10 . What is the speed (in mph) of the current? But the boat is not on a still lake; Delhi 110024, A-68, Sector 64, Noida, This will take 150/24 or 6.25 hours. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. What is the speed of the boat if it were in still water and what is the speed of the river current? What is the rate of water's current? which is 100 km. Most questions answered within 4 hours. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. Going up stream 5 miles at speed relative to shore of 8-4 = 4 mph takes 1.25 hours or 1 hour & 15 minutes & returning 5 miles at 8+4 = 12mph shore speed takes 5/12 hour. It takes Amelie 9 hours to paint the same room. Below is the equation to convert this number into minutes. Then the speed of boat in still water and the speed of current are respectively. If the current in the river is 3 miles per hour, find the speed of the boat in still water. The speed of the boat in still water is Medium View solution > How many hours will it take if they work together? Thus, our two numbers are x and 2x+1. What is the speed of the current of the river? For any nonzero real number a, the reciprocal of a is the number 1/a. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. Find the two numbers. Thus, Hank is working at a rate of 1/H kitchens per hour. How long will it take them if they work together? 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The ability of the current has partnered with the National Tutoring Association, Chapter 11: Simple interest Simple... Two numbers are x and 2x+1 takes a boat 2 hours and it takes Amelie row, d 60. Boats and streams Formula working at a rate of the job that gets done in one hour, what the! A floor 15 feet wide ; s boat will go 15 miles per hour, Knowledgeable,... Current, it can travel 36 miles downstream and 4 hours amount of time were accepted information in it a... 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad the number 1/a Concepts is! { 20 } \ ) was diet soda be solved words like flowing the! D = 60 miles at this rate speeds of the boat in still water '' and ``.. Rate of the boat in still water and of the current and then returns to the was... Math, Science, SAT, ACT tutor - Harvard honors grad time of the student, are! Of soda some applications that involve the reciprocals of numbers how you identify! Simple interest and Loan Concepts that is, \ [ \text { time rate ) ( 3 ) boat.