If it would take one machine 10 minutes to fill a large production order and another machine 12 minutes...

BTGmoderatorLU wrote: ↑

Tue Nov 17, 2020 4:11 pm

Source: GMAT Prep

If it would take one machine 10 minutes to fill a large production order and another machine 12 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?

A. 4 1/60
B. 5
C. 5 5/11
D. 5 1/2
E. 11

The OA is C

With most work questions, a useful approach is to assign a "nice" value to the total job.
We want a number that works well with the given numbers, 10 and 12

So, let's say the production order consists of making 120 widgets

It would take one machine 10 minutes to fill the production order
Rate = output/ time = 120/10 = 12 widgets per minute

It would take the other machine 12 minutes to fill the production order
Rate = output/ time = 120/12 = 10 widgets per minute

COMBINED rate of both machines = 12 + 10 = 22 widgets per minute

How many minutes would it take both machines working together, at their respective rates, to fill the order?
Time = output/rate = 120/22 = 60/11 = 5 5/11 minutes

Answer: C

Cheers,
Brent

BTGmoderatorLU wrote: ↑

Tue Nov 17, 2020 4:11 pm

Source: GMAT Prep

If it would take one machine 10 minutes to fill a large production order and another machine 12 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?

A. 4 1/60
B. 5
C. 5 5/11
D. 5 1/2
E. 11

The OA is C

Solution:

The rate of the first machine is 1/10, and the rate of the second machine is 1/12. Therefore, their combined rate is 1/10 + 1/12 = 6/60 + 5/60 = 11/60. Since time is inverse of rate, the time needed to fill the order when both machines are working together is 1/(11/60) = 60/11 = 5 5/11 minutes.

Answer: C