Question

Mark (✓) against the correct answer:
A can finish a piece of work in 12 hours while B can finish it in 15 hours. How long will both take to finish it, working together?
(a) 9 hours
(b) $6\frac{2}{3}$ hours
(c) $6\frac{3}{4}$ hours
(d) $8\frac{1}{3}$ hours

Answer 1

(b) $6\frac{2}{3}hours$

$$\begin{gathered} \mathrm{A}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{12} \\ \mathrm{B}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{15} \\ (\mathrm{A}+\mathrm{B})\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{12}+\frac{1}{15}=\frac{9}{60}=\frac{3}{20} \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{together}=\frac{20}{3}=6\frac{2}{3}\mathrm{hours} \end{gathered}$$