Sue, an experienced shipping clerk, can fill a certain order in 9 hours. Felipe, a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order?

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Answer 1 · 2017-01-09T07:16:51

#4# hours and #57# minutes.

Here's one method:

The least common multiple of #9# and #11# is #99#.

In #99# hours, Sue could fill #99/9 = 11# orders, while Felipe could fill #99/11 = 9# orders, making a total of #9+11 = 20# orders if they both work.

So for both of them working to fill one order would take:

#99/20# hours.

To express in hours and minutes:

#99/20 = 80/20+19/20 = 4+(3*19)/(3*20) = 4+57/60#

That's #4# hours and #57# minutes, since a sixtieth of an hour is one minute.