Question

If it takes Laine 3 hours to wash the windows, Leslie 4 hours to wash the same windows, and Lance 5 hours to wash the windows, how long would it take them all working together? O 5 hours O 2.6 hours O 0.78 hours O 1.3 hours

Answer 1

Given

Laine - 3 hours

Leslie - 4 hours

Lance - 5 hours.

Let x be the amount of hours it would take when all three of them work together.

Add the sum of the rate of work and equate it to one over x

$\begin{gathered} \frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{1}{x} \\ \frac{4\cdot5}{60}+\frac{3\cdot5}{60}+\frac{3\cdot4}{60}=\frac{1}{x} \\ \frac{20+15+12}{60}=\frac{1}{x} \\ \frac{47}{60}=\frac{1}{x} \\ \frac{60}{47}=\frac{x}{1} \\ x=\frac{60}{47} \\ x\approx1.2766 \end{gathered}$

Rounding to one decimal place, the hours it takes is 1.3 hours.