How long does it take the second worker to do the same job alone?

Question

one custodian cleans a suite of offices in 4 hours. When a second worker is asked to join the custodian it takes the both of them 2&2/3 hours. How long does it take the second worker to do the same job alone

Answer 1

first custodian does the job in 4 hours

his rate is 1/4 of the job done in 1 hour

second custodian does the job in x hours

his rate is 1/x of the job done in 1 hour

together they do the job in 2 2/3 hours, or 8/3 hours

(1/4)(8/3)+(1/x)(8/3)=1 (job finished)

(2/3)+(8/3x)=1

multiply both sides by 3x

(2/3)(3x)+(8/3x)(3x)=1(3x)

2x+8=3x

8=3x-2x

x=8 hours working alone for the second worker

check: (1/4)(8/3)+(1/8)(8/3)=1

           (2/3)+(1/3)=1

                           1=1