A motorboat takes 5 hours...

Question

A motorboat takes 5 hours to travel 150 miles going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Rate of the boat in still water:

Rate of the current:

Answer 1

Hi Kristen,

Assume the current flows at a constant rate and the speed of the boat in still water is constant.

Then, Let x = the rate of the current.

Speed going upstream is 30mph (150 / 5).

Speed going downstream is 50mph (150 / 3)

Two equations can now represent the rate of the boat in still water (upstream) 30 + x (downstream) 50 - x

Set the two equations equal to each other. 30 + x = 50 - x;

Combine like terms and solve for x. 2x = 20; x = 10 (rate of current)

Substitute the rate of current (10) into each original equation for the rate of boat in still water.

30 + 10 = 40 mph. 50 - 10 = 40 mph

So,

The Rate of the boat in still water = 40 mph

The Rate of the current = 10 mph.

Take care,

Tom

Answer 2

d = r * t

150_upstream = (b - c)5

150_downstream = (b + c)3

30 = b - c

50 = b + c

80 = 2b

40 = b

Can you determine the speed of the current and answer?