A motorboat maintained a constant speed of 20 miles per hour relative to the water in going 21 miles upstream and then returning. The total time for the trip was 2.5 hours. Use this information to find the speed of the current.
+128475 Let the speed of the current be = R
Speed with current = 20 + R
Speed against current = 20 - R
And....... Distance / Rate Time
So
21 / (20 + R) + 21 / ( 20 - R) = 2.5 simplify
21 ( 20 - R) + 21(20 + R) = 2.5 ( 20 + R) (20 - R)
420 + 420 = 2.5 ( 400 - R^2)
840 = 2.5 (400 - R^2) divide both sides by 2.5
336 = 400 - R^2
R^2 = 400 - 336
R^2 = 64 take the positive root
R = sqrt (64) = 8 ( mph)
