Question

A motorboat takes 40 minutes to travel 20 miles downstream. The return trip takes 60 minutes. What is the speed of the current?

Answer 1

Hello!

`\large\boxed{c = 5 mph}`

Recall that:

distance = speed × time

In this instance, the distance going downstream and upstream is equal. All we need to do is express speed to solve:

Find the speed going upstream and downstream:

20 / 40 = 1/2 mi / min * 60 min / 1 hour = 30 mph

20 / 60 = 1/3 mi / min * 60 min / 1 hour = 20 mph

Find the speed of the current by expressing a downstream current as + c and upstream current as -c. The speed of the boat (s), without current, would be the same.

s + c = 30

s - c = 20

We can isolate s to solve for c:

s = 30 - c

s = 20 + c

Set the two equations equal to each other:

30 - c = 20 + c

Add c to both sides:

30 = 20 + 2c

Subtract 20 from both sides:

10 = 2c

Divide both sides by 2:

c = 5 mph.