solving a distance, rate, time word problem

Question

A motorboat takes
4
hours to travel
128km
going upstream. The return trip takes
2
hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

Hi Lyn, the distance traveled upstream is the same as the distance downstream. Set up two equations to represent the trip upstream and downstream.

 

Let b represent the boat and r represent the river.

 

Equation 1, upstream:

 

128 = (b - r) * 4, or 128 = 4b - 4r

 

Equation 2, downstream:

 

128 = (b + r) * 2, or 128 = 2b + 2r

 

Solve:

 

4b  - 4r = 128

2b + 2r = 128

----------------

 

Multiply the second equation by 2 and add:

 

4b  - 4r = 128
4b + 4r = 256
----------------

8b = 384

 

b = 48

 

The speed of the boat is 48 kilometers per hour.

 

Substitute for b in equation 1:

 

4 * 48 - 4r = 128

 

192 - 4r = 128

 

-4r = -64

 

r = 16

 

The rate of the river is 16 kilometers per hour.

 

Check using equation 2:

 

2 * 48 + 2 * 16 = 128

 

96 + 32 = 128

 

128 = 128

 

Values check.

 

Questions?