Question

One grocery clerk can stock a shelf in 20 min. A second clerk requires 45 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?

Answer 1

Answer:

clerk A and clerk B can simultaneously stock a shelf in $\frac{180}{13}$ minutes

Explanation:

Let the first clerk be A and the second clerk be B

A can stock a shelf in 20 min

B can stock a shelf in 45 min

Consider the complete work to be W

A’s rate of stocking = $\frac{W}{20}$ per minute

B’s rate of stocking = $\frac{W}{45}$ per minute

When, A and B work simultaneously, rate of work done = $\frac{W}{20}+\frac{W}{45}$

Total work done simulatenously = $\frac{W}{\frac{W}{20}+\frac{w}{45}}$

=$\frac{20 * 45}{20+45}$

Therefore, clerk A and clerk B can simultaneously stock a shelf in $\frac{180}{13}$ minutes