Question

A carpenter can do a job in eight hours. His assistant can do the same job in ten hours. How long would it take them to do the job together?

Answer 1

Answer:

it will take them about 4.44 hours to complete the job when they work together

Step-by-step explanation:

If carpenter B can complete the job in 8 hours, then the portion (fraction) of the job done in the unit of time (one hour) by this carpenter is 1/8

The assistant A can complete the same job in 10 hours, so the fraction of the job done by him in one hour is: 1/10

When they work together, we don't know what time it will take (we name it "x" hours). Therefore the fraction of the job dome in these x hours would be: 1/x

Now we can set the equation that says that the fraction of the job done by B in the unit of time plus the fraction done by A should equal the fraction completed when they work together:

$\frac{1}{8} +\frac{1}{10}=\frac{1}{x}\\\frac{5}{40} +\frac{4}{40}=\frac{1}{x}\\\frac{9}{40}=\frac{1}{x}\\\\x=\frac{40}{9} \\x=4.444...$

Therefore, it will take them about 4.44 hours to complete the job when they work together.