Word problem

Question

One custodian cleans a suite of offices in 5 hours. When a second worker is asked to join the regular custodian, the job takes only 3 and one third hours. How long does it take the second worker to do the same job alone?

Answer 1

1st custodian takes 5 hours alone so he does 1/5 of the job per hour

2nd custodian does x part of the job per hour

The sum of these multiplied by 3 1/3 hours completes the job

 

(1/5 + x)(3 1/3) = 1

(1/5 + x )(10/3) = 1

1/5 + x = 3/10

x = 3/10 - 1/5 = 1/10

 

The 2nd custodian completes 1/10 of the job per hour so it

would take him 10 hours to do the job alone