GMAT question

ironsheep

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Each machine has the same constant rate at a factory. 4 machines work together and take 30 hours to fill out an order, if 5 machines worked together how many fewer hours does it take?? The answer is 6 hours as (4 times 30) divided by 5 equals 24. 30 minus 24 equals 6.


For me, I did 30 divided by 4 equals 7.5, which is the rate that each machine can work. 7.5 times 5 equals 37.5 and 37.5 minus 30 equals 7.5. I did 30 divided by 4 because I wanted to find the rate of each machine. I don't get why they multiplied 30 and 4 together and then divide everything by 5.
 
Each machine has the same constant rate at a factory. 4 machines work together and take 30 hours to fill out an order, if 5 machines worked together how many fewer hours does it take?? The answer is 6 hours as (4 times 30) divided by 5 equals 24. 30 minus 24 equals 6.


For me, I did 30 divided by 4 equals 7.5, which is the rate that each machine can work. 7.5 times 5 equals 37.5 and 37.5 minus 30 equals 7.5. I did 30 divided by 4 because I wanted to find the rate of each machine. I don't get why they multiplied 30 and 4 together and then divide everything by 5.
The job takes (4 * 30 =) 120 machine hours to complete.

So 5 machines will finish the job in (120/5 =) 24 hours.

Continue......
 
The job takes (4 * 30 =) 120 machine hours to complete.

So 5 machines will finish the job in (120/5 =) 24 hours.

Continue......



That is what the book said, but can you please explain in detail why you mulitply the 4 and 30 together???
 
Each machine has the same constant rate at a factory. 4 machines work together and take 30 hours to fill out an order, if 5 machines worked together how many fewer hours does it take?? The answer is 6 hours as (4 times 30) divided by 5 equals 24. 30 minus 24 equals 6.

For me, I did 30 divided by 4 equals 7.5, which is the rate that each machine can work. 7.5 times 5 equals 37.5 and 37.5 minus 30 equals 7.5. I did 30 divided by 4 because I wanted to find the rate of each machine. I don't get why they multiplied 30 and 4 together and then divide everything by 5.
I understand why you would divide 30 by 4 and think that was the rate (hours per machine); but machines working together don't combine that way! You would do that division, for example, if you were making machines (one at a time) and it took 30 hours to make 4. Making more takes longer. But here, more machines working together take less time, because they are working simultaneously, not sequentially.

One way to express this is that the amount of effort required to fill one order can be measured in machine-hours: one machine working for one hour. Four machines working for one hour do 4 times as much work as one (4 machine-hours); and 4 machines working for 30 hours do 30 times that much work (120 machine-hours to fill one order). So we multiply the number of machines by the time that each works, to get the amount of work done. Then if 5 machines work together, how long will it take to fill an order? They need to do 120 machine-hours of work; 120/5 = 24 machines.

The rate that is actually involved here is "orders per machine-hour", not "machines per hour".

A similar issue arises in electronics, where resistances add in series (one after another), but their reciprocals add when they are in parallel (sharing the load) You always have to pay attention to how the numbers combine, and not just do what you would do in a different kind of problem.
 
I understand why you would divide 30 by 4 and think that was the rate (hours per machine); but machines working together don't combine that way! You would do that division, for example, if you were making machines (one at a time) and it took 30 hours to make 4. Making more takes longer. But here, more machines working together take less time, because they are working simultaneously, not sequentially.

One way to express this is that the amount of effort required to fill one order can be measured in machine-hours: one machine working for one hour. Four machines working for one hour do 4 times as much work as one (4 machine-hours); and 4 machines working for 30 hours do 30 times that much work (120 machine-hours to fill one order). So we multiply the number of machines by the time that each works, to get the amount of work done. Then if 5 machines work together, how long will it take to fill an order? They need to do 120 machine-hours of work; 120/5 = 24 machines.

The rate that is actually involved here is "orders per machine-hour", not "machines per hour".

A similar issue arises in electronics, where resistances add in series (one after another), but their reciprocals add when they are in parallel (sharing the load) You always have to pay attention to how the numbers combine, and not just do what you would do in a different kind of problem.


4 machines take 30 hours to get a job done and lets say that they made 9 cars from those 30 hours. 7.5 is wrong as a rate because that would mean that every 7.5 hours, one machine puts out something??? I am having a hard time wrapping my head around all of this. I am having a hard time understanding how to think simultaneously
 
That is what the book said, but can you please explain in detail why you mulitply the 4 and 30 together???
What hours of machine time were needed?

Well the whole order was completed in 30 hours with four machines working equally effectively. That is
4 * 30 = 120 hours of work. So if one machine were working, it would take 120 hours to complete the order.

In other words, proportion of work done by 1 machine per hour = 1/120.

So proportion of work done by 5 machines per hour = 5/120.

Therefore hours per team of 5 machines = 120/5 = 24 hours.



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I think I figured it out after looking at bits and pieces of everyone's response.

Each machine is working 30 hours to get the job done and since there are 4 of them that means 4 times 30 equals 120 hours total. It took 120 hours just to get the job done. That means 120 divided by 5 machines equals 24 hours per machine. The output or units that the machines make-- doesn't matter.
 
Is what I wrote correct??
Yes. I would write that it took 1 machine 120 hours to get the job done so it takes 5 machines working equally effectively 120/5 hours = 24 hours to get the job done.
 
Units are very important. If you used units you would've seen that your original approach was incorrect. Rate is not measured in hours.
 
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