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-Julie and Eric row their boat (at a constant speed) 40 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current.
A) 2.5 mph
B) 4 mph
C) 3 mph
D) 7 mph

Question

Quizplus · Accepted Answer

Let the rate at which they row in still water be x and the rate of the current be y.
When rowing downstream, their effective speed is x+y, so distance traveled is (x+y) * 4 = 40 miles. This gives us the equation 4x + 4y = 40.
When rowing upstream, their effective speed is x-y, so distance traveled is (x-y) * 10 = 40 miles. This gives us the equation 10x - 10y = 40.
Solving these two equations simultaneously gives us x=7 mph (rate at which they row in still water) and y=3 mph (rate of the current). Therefore, the answer is choice C, 3 mph. Let the speed of the boat be B and the speed of the current be C. Then, the speed downstream is B + C and the speed upstream is B - C.

Using the formula Distance = Rate x Time, we get:

Distance downstream = (B + C) x 4 = 40
Distance upstream = (B - C) x 10 = 40

Simplifying these equations, we get:

B + C = 10
B - C = 4

Adding these equations gives us:

2B = 14
B = 7

Substituting B back into one of the equations gives us:

7 + C = 10
C = 3

Therefore, the rate of the current is 3 mph.

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