Chapter 11.5, Problem 23PPE

To determine

If Marian and Robin work together, how long will be the weeding take them.

Answer to Problem 23PPE

1 and $\frac{5}{7}$ hours.

Explanation of Solution

Given:

Marian can weed a garden in 3h.

Robin can weed the same garden in 4h.

Concept used :

• If A can do a piece of work in n hours then A’s one hour’s work = $\frac{5}{7}$
• If B can do a piece of work in m hours then B’s one hour’s work = $\frac{1}{m}$ .
• Then both A and B together complete the work in hours= $\frac{1}{\frac{1}{n}+\frac{1}{m}}$

Calculations :

Weeding done by Marian in 1h.= $\frac{1}{3}$

Weeding done by Robin in 1h.= $\frac{1}{4}$

If both works together then they complete the weeding in hours =

  $\begin{array}{l}=\frac{1}{\frac{1}{3}+\frac{1}{4}}\\ =\frac{1\cdot 12}{\frac{1}{3}\cdot 12+\frac{1}{4}\cdot 12}\\ =\frac{12}{\frac{12}{3}+\frac{12}{4}}\\ =\frac{12}{4+3}\\ =\frac{12}{7}\\ =1\frac{5}{7}\end{array}$