A motorboat can maintain a constant speed of 17 miles per ho

A motorboat can maintain a constant speed of 17 miles per hour relative to water. The boat makes a trip upstream to certain point in 39 minutes; the return trip takes 12 minutes. What is the speed of the current?

The speed of the current is____ miles per hour.

Solution

Let x = speed of the current
then
(17 - x) = speed upstream
and
(17 + x) = speed downstream

Convert 39 min to hrs 39/60 = 13/20 hrs
Convert 12 min to hrs 12/60 = 1/5 hrs

Now, distance = time x speed
then 1/5 (17+x) = 13/20 (17-x)
Multiply both sides 20 to get rid of the denominators:
4(17 + x) = 13(17-x)

68 + 4x = 221 - 13x

13x + 4x = 221 - 68

17x = 153

x = 9
x = 9 mph is the speed of current