Word Translations: Ch. 3 (Ratios), Problem #15

[dk]

Word Translations: Ch. 3 (Ratios), Problem #15 (4th ed)

4 sewing machines can sew shirts in the ratio 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 three machines to sew a total of 3 shirts?

(1) Can you please explain why you can set the ratio equal to the rate as shown in the answer? What is the equation/relationship that makes the below equation possible?

5x=1/2

(2) The way the question is phrased -- "fastest machine can sew a shirt in 2 hours" -- makes it sound like each machine works on an individual basis to sew the shirts. Based on that interpretation, I thought that each machine was used to sew one shirt a piece, ultimately completing 3 shirts. How do you know that this is a "working together" problem?

Thanks in advance for your help.

[jnelson0612]

Word Translations: Ch. 3 (Ratios), Problem #15 (4th ed)

4 sewing machines can sew shirts in the ratio 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 three machines to sew a total of 3 shirts?

(1) Can you please explain why you can set the ratio equal to the rate as shown in the answer? What is the equation/relationship that makes the below equation possible?

5x=1/2

(2) The way the question is phrased -- "fastest machine can sew a shirt in 2 hours" -- makes it sound like each machine works on an individual basis to sew the shirts. Based on that interpretation, I thought that each machine was used to sew one shirt a piece, ultimately completing 3 shirts. How do you know that this is a "working together" problem?

Thanks in advance for your help.

Check out this thread: sewing-machine-t2686.html I think it will answer your first question.

As for the second question, I can see where you are coming from. However, the GMAT would not make that interpretation, because there is no work for you to do in that scenario and the GMAT likes to have you earn your points! In the interpretation you mention, we would just pick the amount of time for the slowest machine to sew one shirt, assuming that the next two faster shirts have already completed one shirt each in that time frame and are sitting idle. In this scenario, you can assume that the GMAT wants you to have the machines work together to make shirts. The overwhelming majority of rates and work problems involve machines or people working together to complete a task. Always err on the side of assuming that.