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} (1)/(3)+(1)/(4)+(1)/(5)=(1)/(x) \\ (4\cdot5)/(60)+(3\cdot5)/(60)+(3\cdot4)/(60)=(1)/(x) \\ (20+15+12)/(60)=(1)/(x) \\ (47)/(60)=(1)/(x) \\ (60)/(47)=(x)/(1) \\ x=(60)/(47) \\ x\approx1.2766 \end{gathered}`

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