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 $7 \frac{2}{3}$ $7 2/3$ hours or $7$ $7$ hours and $40$ $40$ minutes

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

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

So if they work together, then after one hour:

$\frac{1}{14} + \frac{1}{17}$ $1/14+1/17$ of the order will have been completed.

$= \frac{17 + 14}{14 \times 17}$ $= (17+14)/(14xx17)$

$= \frac{31}{238}$ $=31/238$

To complete the whole task, a whole, or $1 or \frac{238}{238}$ $1 or 238/238$ will take:

$\frac{238}{238} \div \frac{31}{238}$ $238/238 div 31/238$

$= 1 \times \frac{238}{31}$ $= 1 xx 238/31$

$= 7 \frac{21}{31}$ $=7 21/31$ hours

$= 7$ $= 7$ hours and $40.6$ $40.6$ minutes