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Rate & Work problem

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Rate & Work problem

by shivshankar054 » Sat Apr 20, 2013 8:27 am

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Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?

A.2
B.3
C.4
D.6
E.9
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by neha24 » Sat Apr 20, 2013 8:37 am
additional machine wud be 4 hence C
12x8=6x total new no of machines
----> total new number of machine wud be =16
so extra wud be 4
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by Anju@Gurome » Sat Apr 20, 2013 10:26 am
shivshankar054 wrote:Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?
12 machines complete the shipment in 8 days.
So, we need 12*8 machine-days to complete the shipment.

Now, the shipment need to be completed in (8 - 2) = 6 days.
Hence, 12*8/6 = 8*2 = 16 machines required.
Therefore, (16 - 12) = 4 more machines are required.

The correct answer is C.
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by GMATGuruNY » Sat Apr 20, 2013 1:10 pm
shivshankar054 wrote:Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?

A.2
B.3
C.4
D.6
E.9
The shipment is to be completed in 6 days instead of 8.
6/8 = 3/4.
Time and rate are RECIPROCALS: to complete the shipment in 3/4 the time, the work must be produced at 4/3 the rate.
Thus, the number of machines must increase by 1/3:
(1/3)12 = 4.
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by Jeff@TargetTestPrep » Mon Dec 18, 2017 11:48 am
shivshankar054 wrote:Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?

A.2
B.3
C.4
D.6
E.9
We are given that 12 machines have a rate of 1/8. We want the shipment to be completed in 6 days, which means that the rate would be â…™. We need to determine the number of machines necessary to have that rate of 1/6. We can create the following proportion in which n = the new number of machines:

12/(1/8) = n(/1/6)

Multiplying the left side by 8/8 and the right side by 6/6, we get:

96 = 6n

16 = n

Thus, there would need to be 4 additional machines.

Answer: C

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