Question

Tom and Jerry can mow the Steeleford Estate in 3 hours when working together. Jerry can complete the mowing in x hours when working alone. Tom would take twice as long as Jerry to do this job. How long would it take each of them to mow the estate alone?

Answer 1

Both Tom and Jerry can mow the estate in 3 hours

Jerry alone can mow the estate in x hours; Jerry's rate = 1/x mow/hour

Tom would mow the estate in 2x hours; Tom's rate = 1/2x mow/hour

$\begin{gathered} \frac{1}{x}+\frac{1}{2x}=\frac{2+1}{2x}=\frac{3}{2x} \\ So,\text{ it follows that,} \\ \frac{2x}{3}=3 \\ \text{cross multiply to get,} \\ 2x=3\times3 \\ 2x=9 \\ x=\frac{9}{2}=4.5\text{ hours} \end{gathered}$

Jerry would take 4.5 hours to mow the estate, while

Tom would take 2x4.5 = 9 hours to mow the estate.