Maria, an experienced shipping clerk, can fill a certain order in 14 hours. Jim, a new clerk, needs 17 hours to do the same job. Working together, how long will it take them to fill the order?

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Answer 1 · 2018-05-21T15:43:00

About $7 2/3$ hours or $7$ hours and $40$ minutes

Consider how much of the task each would complete in one hour:

Maria will complete $1/14$ of the order in one hour.
Jim will complete $1/17$ of the order in one hour.

So if they work together, then after one hour:

$1/14+1/17$ of the order will have been completed.

$= (17+14)/(14xx17)$

$=31/238$

To complete the whole task, a whole, or $1 or 238/238$ will take:

$238/238 div 31/238$

$= 1 xx 238/31$

$=7 21/31$ hours

$= 7$ hours and $40.6$ minutes