Question

One gardener can mow a golf course in 4 hours, while another gardener can mow the same golf course in 6 hours. How long would it take if the two gardeners worked together to mow the golf course?

Short answer

If both gardeners work together then they take 2.4 hours= 2hours 24 minutes.

Step-by-step solution

Given information

The time taken by the gardeners to work is given and the time is asked when they both work together.

Form the equation and solve

Use the given sentence to form the required equation.

• As per the formula, the total time(t) taken by the first gardener(G1) and another gardener(G2) both together can be determined by $\frac{1}{G1}+\frac{1}{G2}=\frac{1}{t}$.
• Substitute the total time taken by gardeners into equation (1) and solve it to find the total time.

$\begin{array}{rcl}\frac{1}{G1}+\frac{1}{G2}& =& \frac{1}{t}\\ \frac{1}{6}+\frac{1}{4}& =& \frac{1}{t}\\ \frac{6+4}{6\times 4}& =& \frac{1}{t}\\ \frac{10}{24}& =& \frac{1}{t}\\ t& =& \frac{24}{10}\\ & =& 2.4hours\\ & =& 2hoursand24minutes\end{array}$