This problem is in Preparation guide - word translations

4 sewing machines can sew shirts in the raito 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.

I am having difficulty in understanding what the ratio means - is it the number of shirts a machine sews in 1 hour or is it the productivity of the machine? If it is the number of shirts in an hour - the last machine would be sewing 5/11 of shirt in a hour which means it sews 10/11 in 2 hours - however it also says the fastest can sew a shirt in 2 hours?

Thanks
Jay

The ratios are comparing the 4 different sewing machines productivity. So if the fastest machine (1:2:3:5) can sew 1 shirt in 2 hours that means it can sew 5 shirts in 10 hours. Now all you have to do is use that logic to say that the other machines ratios are as follows : 1 shirt / 10 hours , 2 shirts / 10 hours, 3 shirts / 10 hours.
(1/10)+(2/10)+(3/10) = So combined they can do 6 shirts in 10 hours.
The questions asks how many hours will it take them to sew 3 shirts?
6/10=3/x
x=5 hours

Hope it helps...

KT

hi -

the first thing that you should realize is that the ratio given in the problem is just that: a ratio. the actual numbers 1, 2, 3, 5 don't have to, and almost certainly don't, represent quantities whose actual values are 1, 2, 3, and 5; they represent proportions.

with that view in mind, then, the ratio in question actually stands for both of the quantities you propose. for if the actual numbers of shirts sewn in some fixed number of hours are in a ratio of 1:2:3:5, then so will be the rates of productivity.

incidentally, rate of productivity in this problem would be defined as shirts per hour, anyway, so there's effectively no difference between the number of shirts sewn in one hour and the productivity rate of the machine.

so:

in this problem you have that the fastest machine sews 1 shirt in 2 hours, for a rate of 1/2 shirt per hour, or 0.5 shirt per hour. so:

first : second : third : 0.5 = 1: 2 : 3 : 5
first = 0.1 shirt/hr
second = 0.2 shirt/hr
third = 0.3 shirt/hr
all together = 0.6 shirt/hr

rate * time = output
(0.6 shirt/hr) * time = 3 shirts
time = 3 / 0.6
5 hours

my my, those are some slow machines.

Thanks for the responses - got it I was not reading it the right way.

can someone pls explain how to understand the ratios. In this case 1:2:3:5, if the given ratio is the no. of hrs a machine takes to sew a shirt, then isnt "1" the fastest machine?

I'm having difficutly understanding these kind of ratio problems

No. The numbers tell us, proportionately, the number of shirts per unit time the four machines are able to produce. As a result the machine that corresponds to 5 in the ratio is the fastest... it sews 5 shirts in the time that it takes the slowest machine to sew 1 shirt.

Rey

How did you get from this line: first : second : third : 0.5 = 1: 2 : 3 : 5 to first = 0.1 shirt/hr, second = 0.2 shirt/hour...and so on?

The machines sew shirts in a ratio of 1:2:3:5. So the fastest machine sews 5 shirts for every 1 shirt the slowest machine sews. The slowest machine gets 1/5 as many shirts done in an hour as the fastest machine.

We are also told that the fastest machine sews a shirt in two hours. Thus, the fastest machine's rate is 1/2. The slowest machine's rate is 1/5 of 1/2, or 1/10 (.1). The next fastest machine is twice as fast as the slowest machine, so its rate is .2 shirts/hr. And so on.

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Jamie Nelson
ManhattanGMAT Instructor