Solve the problem and answer the question.
-A barge takes 6 hours to move (at a constant rate) downstream for 60 miles, helped by a current of 2 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current.
A) 8 hr
B) 10 hr
C) 120 hr
D) 6 hr

Question

Quizplus · Accepted Answer

The barge's speed downstream is: 
speed = distance/time = 60/6 = 10 mph

The current's speed is 2 mph, so the barge's speed upstream is: 
speed = 10 - 2 = 8 mph

The distance to travel upstream is the same 60 miles, so the time it takes the barge to travel upstream is: 
time = distance/speed = 60/8 = 7.5

Since the answer choices are given in hours, the closest choice is 10 hours (B). Let the speed of the barge in still water be x miles per hour. Then, the speed downstream (with the current) is (x+2) miles per hour, and the speed upstream (against the current) is (x-2) miles per hour.
We can use the formula: Distance = Speed x Time
For the downstream trip: 60 = (x+2) x 6
Solving for x, we get x = 8
For the upstream trip: 60 = (x-2) x t (where t is the time taken)
Substituting x = 8, we get 60 = 6(t-2)
Solving for t, we get t = 10
Therefore, the time of the return trip against the current is 10 hours, which is given by choice B.

Solve the Problem and Answer the Question