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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 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. 27 Sep 2008, 11:49
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amitdgr
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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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!
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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 27 Sep 2008, 18:08
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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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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 27 Sep 2008, 18:30
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agree with leonidas

1/10 + 2/10 + 3/10= 3shirts/5hrs
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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 27 Sep 2008, 18:36
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machine 4 is fastest and it takes 2 hours to sew 5 shirts
we can say 120 /5 = 24 min for 1 shirt

machine 3: 120/3 = 40 min for 1 shirt

machine 2: 120/2 = 60 min for 1 shirt

machine 3: 120/1 = 12 min for 1 shirt


so total time taken by 1,2,3 machine will be

1/120 +1/60 +1/40 = 1+2+3/120 = 6/120 = 1/20

so it takes 1 hour - 60 minute for 20 shirts..will take 9 min. to sew 3 shirts

ha ha... i made some big mistake some where.. it can't be so easy :)
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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 15 Aug 2011, 20:31
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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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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 15 Aug 2011, 21:08
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sgupta0827
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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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.
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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 16 Aug 2011, 03:51
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amitdgr
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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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

Ans: "5 hours"
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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 21 Aug 2011, 08:23
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fastest machine
1 shirt in 2hrs
5 shirts in 2*5 = 10 hrs

3 machines together make 6 shirts in 10 hrs (same time as the fastest takes to make 5 shirts)
time required to make 3 shirts = 5hrs
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4 sewing machines can sew shirts in the ratio of 1:2:3:5. 27 Nov 2025, 08:49
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