Math 3 Motorboat question

Question

A motorboat in still water was traveling 8 mph. It made a round trip in a river 10 miles in 6 hours. Dertemine the rate of the current in the river.

Answer 1

Let v_b = 8 mph and v_c be the speed of the current. Since the trip is a round trip, one direction will be with the current and the other direction against it. The total time, therefore, to complete the round trip is

T = (10 mi)/(v_b + v_c) + (10 mi)/(v_b - v_c) = 6 hr

Letting v_c = x we have

(3/5)hr/mi = 1/(8 +x) + 1/(8-x) or (3/5)(64 - x²) = (8-x) + (8 +x) = 16. So x = sqrt(112/3) = 4sqrt(7/3)