machines

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sgr21: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Oct 21, 2013 12:52 am

by sgr21 » Mon Jun 02, 2014 12:22 am

Machine A & machine B working together can finish producing a container load of widgets in 7 1/7 hours. Machine A can alone finish producing a container load of widgets in 10 hours and machine B can alone finish producing the same in 25hours. both machine A and B are started together to produce a container load of widgets . However after 3 hours machine B develops a malfunction and starts producing widgets at half speed. how many more hours will it take for both machine A and B to together complete producing the container load of widgets after machine B develops malfunction?

A) 5 hours and 15mins
B) 3 hours and 30mins
C) 3 hours and 40mins
D) 4 hours and 50mins
E) 4 hours and 20mins

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Source: Beat The GMAT — Problem Solving | Mon Jun 02, 2014 12:22 am

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by GMATGuruNY » Mon Jun 02, 2014 2:55 am

sgr21 wrote:Machine A & machine B working together can finish producing a container load of widgets in 7 1/7 hours. Machine A can alone finish producing a container load of widgets in 10 hours and machine B can alone finish producing the same in 25hours. both machine A and B are started together to produce a container load of widgets . However after 3 hours machine B develops a malfunction and starts producing widgets at half speed. how many more hours will it take for both machine A and B to together complete producing the container load of widgets after machine B develops malfunction?

A) 5 hours and 15mins
B) 3 hours and 30mins
C) 3 hours and 40mins
D) 4 hours and 50mins
E) 4 hours and 20mins

Let the job = 100 widgets.

Since A can complete the job in 10 hours, A's rate alone = w/t = 100/10 = 10 widgets per hour.
Since B can complete the job in 25 hours, B's rate alone = w/t = 100/25 = 4 widgets per hour.
Combined rate for A and B together = 10+4 = 14 widgets per hour.

In 3 hours, the number of widgets produced by A and B together = r*t = 3*14 = 42 widgets.
Remaining widgets = 100-42 = 58 widgets.

When B's rate is reduced by half, the combined rate for A and B = 10+2 = 12 widgets per hour.
At a rate of 12 widgets per hour, the time for A and B to finish the remaining 58 widgets = w/r = 58/12 hours = 29/6 hours = 4 hours, 50 minutes.

The correct answer is D.

Last edited by GMATGuruNY on Mon Jun 02, 2014 9:23 am, edited 1 time in total.

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by Brent@GMATPrepNow » Mon Jun 02, 2014 7:07 am

sgr21 wrote:Machine A & machine B working together can finish producing a container load of widgets in 7 1/7 hours. Machine A can alone finish producing a container load of widgets in 10 hours and machine B can alone finish producing the same in 25hours. both machine A and B are started together to produce a container load of widgets . However after 3 hours machine B develops a malfunction and starts producing widgets at half speed. how many more hours will it take for both machine A and B to together complete producing the container load of widgets after machine B develops malfunction?

A) 5 hours and 15mins
B) 3 hours and 30mins
C) 3 hours and 40mins
D) 4 hours and 50mins
E) 4 hours and 20mins

While I prefer the method of letting the entire job equal a certain number of widgets (as Mitch has demonstrated), I thought it might be useful that we can also solve the question another way.

Working together, machines A and B can complete the ENTIRE job in 7 1/7 hours.
So, after working for 3 hours, the FRACTION of the job completed = 3/(7 1/7) = 3/(50/7) = 21/50
So, after 3 hours, the fraction of the job REMAINING = 1 - 21/50 = 29/50

At this point, machine B's rate of work is halved. So, machine B, working alone, can complete the ENTIRE job in 50 hours. So, machine B can complete 1/50 of the job in 1 hour.
Likewise, if machine A, working alone, can complete the ENTIRE job in 10 hours, then machine A can complete 1/10 of the job in 1 hour.

So, in 1 hour, the two machines can complete (1/50 + 1/10) of the job
1/50 + 1/10 = 6/50 = 3/25
Their combined RATE = 3/25 of the job per hour

So, the time to complete the remaining 29/50 of the job = (29/50)/(3/25)
= (29/50)(25/3)
= (29/2)(1/3)
= 29/6
= 4 5/6 hours
= 4 hours and 50 minutes
= D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Mon Jun 02, 2014 11:19 am

Hi sgr21,

Since the answer choices are numbers, we can actually take advantage of a minor "shortcut" that's built into this question.

I'm going to build off of Brent's approach - breaking down the "fraction of the job" that each machine does PER HOUR.

Machine A can do the job in 10 hours, so it does 1/10 of the job per hour.
Machine B can do the job in 25 hours, so it does 1/25 of the job per hour.
Together, they do 1/10 + 1/25 = 7/50 of the job per hour

After 3 hours, they've completed 3(7/50) = 21/50 of the job, so 29/50 remains.

Since Machine B's rate becomes half of what it once was, we now have:
Machine A = 1/10 of the job per hour.
Machine B = 1/50 of the job per hour.
Together, they now do 6/50 of the job per hour.

Here's where the shortcut comes in...

29/50 of the job remains; the machines complete 6/50 of the job per hour.

To get from 6/50 to 29/50, we have to multiple by a little less than 5. So, which answer is a little less than 5 hours?

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

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