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