Question

Bill can repair a transmission in 8 hours. It takes Henry 10 hours to do the same job. If they begin the job together and then Bill leaves after 3 hours, how long will it take Henry to finish?

Answer 1

Answer: Henry will take 3.25 hours to finish the work alone.

Explanation

Given

• Bill can repair a transmission in 8 hours.

,

• It takes Henry 10 hours to do the same job.

,

• If they begin the job together and then Bill leaves after 3 hours, how long will it take Henry to finish?​

Procedure

Bill does 1/8 of the job per hour, while Henry does 1/10 of the work per hour. They work together 3 hours. If we assume their works are additive (no interference from one another), and considering that:

$rate\times time=\text{work done}$

Then we can build the following relation:

$(\frac{1}{8}+\frac{1}{10})\times3=\text{ work done}$

Simplifying:

$\text{ work done}=(\frac{5+4}{40})\times3=(\frac{9}{40})\times3=\frac{27}{40}$

The job at the 3 hours will be 27/40 done. Then, Henry has to finish the rest of the work, which is:

$\frac{40}{40}-\frac{27}{40}=\frac{13}{40}$

Finally, to calculate the time it will take Henry to do the job, we have to do the following:

$\frac{1}{10}\times t=\frac{13}{40}$$t=\frac{\frac{13}{40}}{\frac{1}{10}}=\frac{130}{40}=\frac{13}{4}\approx3.25h$