What is the rate of the boat in still water and what is the rate of the current?

Question

A motorboat travels 96 kilometers in 3 hours going upstream. It travels 168 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

B = the speed of the boat in still water.

S = the speed of the stream

Relative to the bank, the speed upstream is B-S.

The speed downstream is B+S.

Use the equation for distance.

Rate * Time = Distance

Upstream

(B-S)3 = 96

(B+S)3 = 168

Simplify first:

B-S = 32

B+S = 56

Solve by elimination. Add the two equations.

2B = 88

B = 44 mi/hr

Substitute this into either equation and solve for S.

B+S = 56

44+S = 56

S = 12 mi/hr