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work problem from gmat prep

by Taniuca » Mon Sep 26, 2011 5:34 pm
six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same rate, will be needed to complete the job in 12 days?
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by Anurag@Gurome » Mon Sep 26, 2011 6:19 pm
Taniuca wrote:six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same rate, will be needed to complete the job in 12 days?
Total work = 12 * 6 = 72 machine days
9 machines will do the work in 8 days (since 9 * 8 = 72)
Therefore, no. of additional machines needed = 9 - 6 = 3
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by Taniuca » Mon Sep 26, 2011 6:39 pm
when we use work rates the books most likely refer to work/time. How could you solve this problem using that concept?
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by Anurag@Gurome » Mon Sep 26, 2011 6:52 pm
Taniuca wrote:when we use work rates the books most likely refer to work/time. How could you solve this problem using that concept?
Work = rate * time * no. of machines
Let the work be 1.
1 = rate * 12 * 6
rate = 1/72

Now everything remains the same except the no. of machines.
work = rate * time * no. of machines
1 = 1/72 * 8 * no. of machines
So, no. of machines = 72/8 = 9
Additional machines required = 9 - 6 = 3
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by zaarathelab » Fri Oct 14, 2011 4:25 am
If 6 machines complete the work in 12 days

Each machine individually has a rate of 1/72 per day.

Now since the machines have to finish the work in 8 days, what should be the individual rate of work per day for each machine = 1/72 * 8 = 1/9

Therefore, we need to have 9 machines to complete the work in 8 days or 3 additional machines are required.
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