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4 sewing machines can sew shirts in the ratio of 1:2:3:5. [#permalink]

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27 Sep 2008, 05:22

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4 sewing machines can sew shirts in the ratio of 1:2:3:5. The fastest can sew a shirt in 2 hours. However the fastest machine breaks. How long will it take the other 3 machines to sew a total of 3 shirts.
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4 sewing machines can sew shirts in the ratio of 1:2:3:5. The fastest can sew a shirt in 2 hours. However the fastest machine breaks. How long will it take the other 3 machines to sew a total of 3 shirts.

How do you determine which is the fastest? 4 sewing machines can sew shirts in 1:2:3:5 is not telling me any thing about how many hours each one is taking to sew a shirt. Just because the 4th sewing machine is showing 5 does not mean that it can sew faster than the other 3.

As usual with MGMAT, they might have some crypt built in, which I am not able to figure out. Comments folks!

Machine one will sew 1 shirt while machine four will sew 5 shirts at the same time, from the ratio given, machine four is the fastst. Machine 4 can sew one shirt in 2 hours=> 5 shirts in 10 hrs. Therefore, machines 1 will take 10 hrs for 1 shirt, machine 2 will take 10/2 hrs for 1 shirt, machine 3 will take 10/3 hrs for 1 shirt.

when all 3 machines are working together for 1 hr will produce = 1/10 + 2/10 + 3/10 = 3/5 shirts. Therefore, it will take 5 hours to sew 3 shirts.
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I got confused about this question on how we can assume that the sewing is in parallel. Is it realistic to have two machines or three machines producing one shirt? I thought the total time that three machines take in sewing 3 shirts will be the time taken by the slowest machine. However, in MGMAT's explanation they have considered all the machines producing shirts at the same time. Can someone please explain?
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I got confused about this question on how we can assume that the sewing is in parallel. Is it realistic to have two machines or three machines producing one shirt? I thought the total time that three machines take in sewing 3 shirts will be the time taken by the slowest machine. However, in MGMAT's explanation they have considered all the machines producing shirts at the same time. Can someone please explain?

In work rate problems, many questions make you assume that work can be divided into infinitesimally small jobs and all machines work on these jobs to complete the work. Practically, I would think that one machine will sew one complete shirt. But since it is a work-rate problem, I would, unhappily, make the assumption that I don't have to worry about how the work will be divided. I just assume that each machine is working on the same shirt at its own rate.

"I thought the total time that three machines take in sewing 3 shirts will be the time taken by the slowest machine."

That would be my first thought too. But then, its not a work-rate problem anymore. Many questions specifically mention something like "All machines can work at the same time on a shirt" to make it clearer.
_________________

4 sewing machines can sew shirts in the ratio of 1:2:3:5. The fastest can sew a shirt in 2 hours. However the fastest machine breaks. How long will it take the other 3 machines to sew a total of 3 shirts.

Combined speed of slower ones: Speed of fastest 1+2+3:5 6:5

5 times fast-> 2*3=6 hours 1 times fast-> 6*5 hours 6 times fast-> 6*5/6 hours= 5 hours

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