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

Let x = rate of boat in still water and let c = rate of the current. Remember that distance = rate × time. To solve this problem, you can set up a table where the first row is the boat's upstream (against the current) journey and the second row is the boat's downstream (with the current) journey:

 

DISTANCE           RATE           TIME

128 km                  x - c             4 hr.

128 km                  x + c            2 hr.

 

Since d = rt, you can set up the following two equations:

 

128 = 4(x-c)

128 = 2(x+c)

 

Solve both equations for c:

 

128 = 4(x-c)

32 = x - c

c + 32 = x

c = x - 32

 

128 = 2(x+c)

64 = x+c

64 - x = c

 

Now, you can substitute c = x - 32 into the second equation and solve for x:

 

64 - x = x - 32

96 - x = x

96 = 2x

48 = x

 

This means that the rate of the boat in still water is 48 km/hr.

 

Finally, substitute x = 48 back into the first equation and solve for c:

 

64 - 48 = c

16 = c

 

This means that the rate of the current is 16 km/hr.