Solve the problem.
-A barge takes 4 hours to move (at a constant rate)downstream for 32 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)6 hours
B)64 hours
C)4 hours
D)8 hours

Question

Quizplus · Accepted Answer

To solve this problem, we can start by using the formula: distance = rate x time.

For the downstream trip: 
distance = 32 miles 
rate = barge's speed + current's speed = x + 2 
time = 4 hours

So we have: 
32 = (x + 2) * 4

Simplifying this equation, we get: 
8 = x + 2 
x = 6

This means that the barge's speed without the current is 6 miles per hour.

Now, for the upstream trip, the barge is going against the current, so its speed is its own speed minus the current's speed: 
rate = x - 2 = 6 - 2 = 4

Let's use the distance formula again: 
distance = 32 miles 
rate = 4 miles per hour 
time = ?

32 = 4 * time 
time = 8

Therefore, the time for the return trip against the current is 8 hours. The answer is D.

Solve the Problem. -A Barge Takes 4 Hours to Move (At a Constant