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

clerk A and clerk B can simultaneously stock a shelf in
`(180)/(13)` minutes

Step-by-step 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 =
`(W)/(20)` per minute

B’s rate of stocking =
`(W)/(45)` per minute

When, A and B work simultaneously, rate of work done =
`(W)/(20)+(W)/(45)`

Total work done simulatenously =
`(W)/((W)/(20)+(w)/(45))`

=
`(20 * 45)/(20+45)`

Therefore, clerk A and clerk B can simultaneously stock a shelf in
`(180)/(13)` minutes