Juan accepted a job to roof a new house. He calculated that he can complete the job in 20 hours. He hired a trainee to assist him. He has seen the trainee work and estimates that the trainee working alone would take 25 hours to complete the job. How much time should the two of them working together need to roof the house? (Round your answer to the nearest tenth.)

Question

calculusxy · Answer

Juan rate + trainee rate
(1/20)+(1/25)=100(1/x)

Times both sides by 100 to isolate
100(1/20)+(1/25)=100(1/x)
100(1/20)+100(1/25)=100/x
5+4=100/x
9=(100/x)

Cross multiply
9*8=100*1
9x=100

Divide both sides by 9
9x/9=100/9
x=1.1111...
Rounded= 11.1

(I had posted this on the same question)

calculusxy · Answer

@shortie18