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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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

$4$ $4$ hours and $57$ $57$ minutes.

Explanation:

Here's one method:

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

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

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

$\frac{99}{20}$ $99/20$ hours.

To express in hours and minutes:

$\frac{99}{20} = \frac{80}{20} + \frac{19}{20} = 4 + \frac{3 \cdot 19}{3 \cdot 20} = 4 + \frac{57}{60}$ $99/20 = 80/20+19/20 = 4+(3*19)/(3*20) = 4+57/60$

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

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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?

1 Answer

Explanation:

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