Rate Problems

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fleischwolf: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Jan 21, 2009 1:40 pm; Thanked: 1 times

by fleischwolf » Sat Mar 07, 2009 4:57 am

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute.

(2) Machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours.

The Answer is B

I'm actually able to solve such problems. However, I need lots of time. Is there an easy rule, how much information you need to solve rate problems? I kind of start in the following way and write down all information I have (including relationships between rate,time, amout produced of X and Y).

Machine X
Rate X
Amout produced X
Time X

Machine Y
Rate Y
Amount produced Y
Time Y

How much information, in general, do I need?

Source: Beat The GMAT — Data Sufficiency | Sat Mar 07, 2009 4:57 am

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Sat Mar 07, 2009 5:17 am

Statement 1 is not sufficient because we don't know the total number of bottles are produced.

Statement 2:
Machine A produced twice as many bottles as machine B.

This means, machine A did 2/3 of the job, and machine B did 1/3 of the job.

From the question stem, machine A spent 4hrs doing its part. So we now know that machine A took 4 hrs to complete 2/3 of the job. We can then calculate how long machine A would have taken to do the whole job by itself, 6 hours. Hence, sufficient.

Choose B.

-BM-

fleischwolf: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Jan 21, 2009 1:40 pm; Thanked: 1 times

by fleischwolf » Sat Mar 07, 2009 5:52 am

Thanks bluementor,

that's a nice and easy way to solve this problem. My way took ages compared to your solution.

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