A motor travels 10 mph in still water. The boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24 miles going downstream. Find the rate of the current.

The rate of the current is 2 mph.

Step-by-step explanation:

When the boat travels upstream we have:

Where:

: is the total speed

: is the speed of the boat = 10 mph

: is the speed of the current

x: is the distance

t: is the time

And when the boat travel downstream we have:

Since the boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24 miles going downstream we have:

  (1)

  (2)

By adding equation (1) with (2):

By solving the above equation for t we have:

t = 2 h      

Now, by entering "t" into equation (2) we have:

Therefore, the rate of the current is 2 mph.

I hope it helps you!