Question

A motorboat travels 282 kilometers in 6 hours going upstream. It travels 402 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

Let,

B = the speed of the boat in still water

S = the speed of the stream

Use the equation for distance.

Rate * Time = Distance

Upstream:

(B-S)6 = 282

Downstream:

(B+S)6 = 402

Simply first:

(B-S)6 = 282

(B-S) = 282/6

B-S=47

(B+S)6 = 402

(B+S) = 402/6

B+S=67

Solve by elimination. Add the two equations.

B-S=47

+ B+S=67

2B = 114

B = 114/2

B = 57 km/hr (the speed of the boat in still water)

Substitute this into either equation and solve for S.

B+S=67

57 + S = 67

S = 67 - 57

S = 10 km/hr (the speed of the stream)