Question

Jimmy can oil the lanes in a bowling alley in eight hours. Perry can oil the same lanes in nine hours. How long would it take them if they worked together?

Answer 1

Answer:

It would take $4\frac{4}{17}$ or 4.24 hours to oil the lanes if they work together.

Step-by-step explanation:

Given:

Time to oil the lanes by Jimmy alone = 8 hours

Time to oil the lanes by Perry alone = 9 hours

Now, let the time taken by both working together be 'x' hours.

Part of the work done in 1 hour by Jimmy alone = $\frac{1}{8}$

Part of the work done in 1 hour by Perry alone = $\frac{1}{9}$

Part of the work done in 1 hour by Jimmy+Perry together = $\frac{1}{x}$

Now, total work in 1 hour is given as:

$\frac{1}{8}+\frac{1}{9}=\frac{1}{x}\\\\\frac{1\times 9}{8\times 9}+\frac{1\times 8}{8\times 9}=\frac{1}{x}\\\\\frac{9+8}{72}=\frac{1}{x}\\\\\frac{17}{72}=\frac{1}{x}\\\\\textrm{Doing cross product, we get:}\\\\17x=72\\\\x=\frac{72}{17}=4\frac{4}{17}\ hours$

Therefore, it would take $4\frac{4}{17}$ or 4.24 hours to oil the lanes if they work together.