SOLUTION: A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point 20 minutes; the return trip take 15 minutes.
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Question 1208940: A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point 20 minutes; the return trip take 15 minutes. What is the speed of the current?
Going against the current (i.e. upstream) the boat's speed goes from 16 mph to 16-c mph.
distance = rate*time
d = r*t
d = (16-c)*(20/60)
d = (1/3)(16-c)
Going with the current (downstream) means the boat goes from 16 mph to 16+c mph.
d = r*t
d = (16+c)*(15/60)
d = (1/4)(16+c)
The two equations involve the same distance.
This allows us to equate the right hand sides to solve for c.
(1/3)(16-c) = (1/4)(16+c)
12*(1/3)(16-c) = 12*(1/4)(16+c)
4(16-c) = 3(16+c)
64-4c = 48+3c
64-48 = 3c+4c
16 = 7c
c = 16/7
c = 2.2857 mph approximately
Side notes:
To convert from mph to miles per minute, divide by 60.
The improper fraction 16/7 converts to the mixed number 2 & 2/7
The solution method from the other tutor is fine, and it is probably what you will find in most references.
Usually, when the distances are the same at two different speeds, the algebra required to find the answer is easier if you use the fact that the speed is inversely proportional to the time. A solution using that starting point is shown below.
Let x be the speed of the current. Then the upstream speed is 16-x and the downstream speed is 16+x.
The distances upstream and downstream are the same. Then, since the ratio of times upstream and downstream is 20:15 = 4:3, the ratio of the upstream and downstream speeds is 3:4. So
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