Question

Daria can weed the garden in 7 hours, while her mother can do it in 3. How long will it take the two of them to work together?

Short answer

They take 2.1 hours= 2 hours and 6 minutes to work both together.

Step-by-step solution

Given information

The time taken by the persons 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 Daria(D) and her mother(M) both together can be determined by $\frac{1}{D}+\frac{1}{M}=\frac{1}{t}...........\left(1\right)$.
• Substitute the time taken by Daria and her mother into equation (1) and solve it to find the total time.

$\begin{array}{rcl}\frac{1}{t}& =& \frac{1}{D}+\frac{1}{M}\\ & =& \frac{1}{7}+\frac{1}{3}\\ & =& \frac{7+3}{7\times 3}\\ & =& \frac{10}{21}\\ T& =& \frac{21}{10}\\ & =& 2.1hours\\ & =& 2hours6minutes\end{array}$