SOLUTION: A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Find th

Let x be the speed of the current, in miles per hour.

The motorboat' speed with the current is 15+x mph,

and against the current is 15-x mph.


Write and use the time equation

     +  = 1.5 hours    (1)

for the total trip.


To solve, multiply both sides by (15-x)*(15+x) = 225 - x^2.  You will get

    10(15+x) + 10*(15-x) =  1.5*(225-x^2),

    300 = 1.5*225 - 1.5*x^2,

    600 = 3*225 - 3x^2,

    3x^2 = 675 - 600,  3x^2 = 75,   x^2 = 75/3 = 25,  

    x =  = 5 mph.


CHECK  equation  (1):    =  = 1 hours = 1.5 hours.


ANSWER.  The current speed is 5 miles per hour.