word problem

Question

One painter can finish a certain job 5 hours before another painter who is doing the same job. When they work together they can finish this job in 6 hours. How long does it take for each painter to do the job by himself?

One painter can finish a certain job 5 hours before another painter who is doing the same job. When they work together they can finish this job in 6 hours. How long does it take for each painter to do the job by himself?

Answer 1

Painter 1 works at a rate of 1/x

 

Painter 2 works at a rate of 1/(x - 5)

 

We have the following equation to represent their combined work rate

 

1/x + 1/(x - 5) = 1/6

 

6(x - 5) + 6x = x(x - 5)

6x - 30 + 6x = x² - 5x

12x - 30 = x² - 5x

x² - 17x + 30 = 0

(x - 2)(x - 15) = 0

 

The only solution that makes sense is x = 15 because x = 2 would give Painter 2 a rate of -3.

 

Painter 1 can do the job in 15 hours alone, and Painter 2 can do the job in 10 hours alone