Solve the problem.
-Julie and Eric row their boat (at a constant speed)35 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of the current.
A)2 mph
B)0.5 mph
C)1 mph
D)6 mph

Question

Quizplus · Accepted Answer

Let the speed of the boat be x and the speed of the current be y.
For the downstream trip, the boat's speed is (x + y) and the distance is 35 miles. Therefore, the time taken is given by:
35/(x+y) = 5
Simplifying this equation, we get:
x + y = 7 --- (1)
For the upstream trip, the boat's speed is (x - y) and the distance is also 35 miles. Therefore, the time taken is given by:
35/(x-y) = 7
Simplifying this equation, we get:
x - y = 5 --- (2)
Adding equations (1) and (2), we get:
2x = 12
x = 6
Substituting x = 6 into equation (1), we get:
6 + y = 7
y = 1
Therefore, the rate of the current is 1 mph. Let the speed of the boat be x miles per hour and the speed of the current be y miles per hour.
35 = (x + y) * 5
35 = (x - y) * 7
Simplifying the equations:
x + y = 7
x - y = 5
Adding both equations, we get:
2x = 12
x = 6
Substituting x in one of the equations:
x + y = 7
6 + y = 7
y = 1
Therefore, the rate of the current is 1 mph.

Solve the Problem. -Julie and Eric Row Their Boat (At a Constant Speed)35