Question

One grocery clerk can stock a shelf in 25 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

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 = per minute

B’s rate of stocking = per minute

When, A and B work simultaneously, rate of work done =

Total work done simulatenously = 180/13

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

Answer 2

Explanation:

The rate of each clerk is 1/25 and 1/45 respectively so together they can stock the shelf

t/25+t/45=1 (the least common multiple of 25 and 45 is 225)

t/25(9/9)+t/45(5/5)=1

(9t+5t)/225=1

9t+5t=225

14t=225

t=225/14 min

t=16 minutes (rounded to nearest minute)

( or 16 minutes and about four seconds :) )