Question

Maria, an experienced shipping clerk, can fill a certain order in 9 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

Answer:

4 19/20 hours or 4 hours , 57 minutes

Step-by-step explanation:

Given

In 9 hours Maria can fill a certain order let Say X

In 9/9 hours Maria can fill   X/9 of the order

in 1 hour Maria can fill   X/9 of the order

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In 11 hours Jim can fill a certain order let Say X

In 11/11 hours Maria can fill   X/11 of the order

in 1 hour Maria can fill   X/11 of the order

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Therefore total order filled by them in one hour will sum of individual work done by them in one hour.

Mathematically,

total order filled by Jim and maria in one hour = work done by Jim in one + work done by Maria in one hour

total order filled by Jim and maria in one hour = 1/11 + 1/9

=> $1/11 + 1/9 \\=> (9 + 11)/11*9\\=> 20/99$

=>20/99 of certain order is filled by both of them in one hour.

=>Total order is one. Hence, to get 1 from 20/99 we need to multiply it with its reciprocal (i.e 99/20) as 20/99 *99/20 = 1

now

=>20/99 of certain order is filled by both of them in 1 hour.

=>multiplying both order and hour with 99/20 we have

20/99 *99/20 of certain order is filled by both of them in 1* 99/20 hour

Thus total order is filled by them in 99/20 hours = 4 19/20 hours.

1 hour has 60 minutes

so 19/20 has 60*19/20 minutes = 57 minutes.

Working together, Jim and Maria   will  take 4 hours , 57 minutes  to fill the order.