Arthur D. answered • 10/28/15

Effective Mathematics Tutor

roofer's rate=1/12 of the job done per hour

apprentice's rate=1/x of the job done per hour

in 8 hours the roofer does 8/12 or 2/3 of the job

the apprentice does the rest of the job which is 1/3 of the job

the apprentice worked for 8 hours at the rate of 1/x and now works for 14 more hours at the rate of 1/x

the apprentice again does only 1/3 of the job

(1/x)(8)+(1/x)(14)=1/3

(8/x)+14/x)=1/3

22/x=1/3

cross multiply

22*3=1*x

x=66 hours

it would take the apprentice 66 hours working alone

check:

8/12+8/66=2/3+4/33=22/33+4/33=26/33 of the job done when the roofer leaves

7/33 of the job is left to do by the apprentice whose rate is 1/66 per hour

if he works for 14 more hours he does 14*(1/66)=14/66=7/33 of the job