Distance Rate Time Problem

Question

A motorboat takes
5
hours to travel
150km
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?

Answer 1

let x be speed of the current

let y be speed of the motorboat

 

so,

 

5(y - x) = 150

 

3(y + x) = 150 ------> (x + y) = 150/3

 

x + y = 50 ------> y = 50 - x

 

substitute y:

 

5(50 - x - x) = 150

 

250 - 10x = 150

 

250 - 150 = 10x

 

100 = 10x

 

x = 10

 

let's use: 5(y - x) = 150 to solve for y:

 

5 (y  - 10) = 150

 

5y - 50 = 150

 

5y = 150 + 50 = 200

 

5y = 200

 

y = 40

 

speed of current is 10 km/hr

speed of motorboat is 40 km/hr