Word problem

Question

Emily can paint her fence in 6 h. If she does the job with her son it takes 2.5 h less. how long would it take her son working alone?

Answer 1

Hi Shophie,

 

If Emily can paint the fence in 6 hrs  she can paint 1/6 of the fence each hour

 

So that is her work rate, we need to find her son's work rate.

 

let x = her son's work rate

 

and we know that working together they can paint the fence in 6 - 2.5 = 3.5 hours

 

so

 

3.5(1/6) + 3.5x = 1

 

(7/2)(1/6) + (7/2)x = 1

 

multiply by 2/7

 

1/6 + x = 2/7

 

x = 2/7 - 1/6

 

x = 12/42 - 7/42

 

x = 5/42   (this is the amount that the son paints each hour

 

The time it would take him on his own is the reciprocal of his rate

 

42/5 = 8.4 hours on his own

 

Hope this helps