Question

Sue, an experienced shipping clerk, can fill a certain order in 6 hours. Jim, a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order?

Answer 1

3 15/17 hours

Explanation:

Sue's rate of completion is ...

1/6 order per hour

Jim's rate of completion is ...

1/11 order per hour

Assuming they can appropriately divide the work, their total rate of completion will be ...

(1/6 + 1/11) = (11+6)/(66) = 17/66 . . . . order per hour

The time for one order is the inverse of that: 1/(17/66) ...

66/17 hours per order = 3 15/17 hours per order

Working together, it will take Sue and Jim 3 15/17 hours to fill the order.