Question

Working together, Adam and Pranav can mop a warehouse in 4.63 hours. Had he done it alone it would have taken Pranav 11 hours. How long would it take Adam to do it alone?

Answer 1

$8hours$

1)

Note that the more people work together the less time they spend.

This is a question about Proportions, Inverse variation. So let's set the ratios and the proportion given these data.

So we can write out the following ratios:

$\begin{gathered} \frac{1}{x}+\frac{1}{11}=\frac{1}{4.63} \\ \\ \frac{x+11}{11x}=\frac{1}{4.63} \\ \\ 4.63(x+11)=11x \\ 11x=4.63(x+11) \\ 11x-4.63x=11 \\ 6.37x=11 \\ \frac{6.37x}{6.37}=\frac{11}{6.37} \\ x=7.99\approx8 \end{gathered}$

So, it would take 8 hours for Adam to do it alone.