Question

Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as fast as Stan, how long does it take Stan to mow the lawn alone?

Short answer

Stan would take 120 minutes to complete the work alone.

Step-by-step solution

Step-1. Determine the quantities.

Let x be the time taken by Hilda and time taken by Stan is y.

Since Hilda work twice as fast as Stan thus, $2x=y$.

Step-2. Set up the model.

Both can mow the lawn in 40 min.

$\begin{array}{l}\frac{1}{x}+\frac{1}{y}=\frac{1}{\frac{40}{60}}\\ \frac{1}{x}+\frac{1}{2x}=\frac{3}{2}\end{array}$

Step-3. Solve for x.

$\begin{array}{l}\frac{1}{x}+\frac{1}{2x}=\frac{3}{2}\\ \frac{2+1}{2x}=\frac{3}{2}\\ 3=3x\\ x=1\end{array}$

The time taken by Hilda is 1 hour so the time taken by Stan must be 2 hours.

Hence, Stan would take 120 minutes to complete the work alone.