OG 12 DS 112

[navalpike]

I have been using Ian's method of solving “work” problems (matching all participant’s number of hours) and it has really helped me. However, in order to stay consistent, I tried the method to solve this problem but failed. Can Ian (or anyone else using Ian’s method) show how to solve this problem by making the hours identical.

The method is also discussed here:
https://www.beatthegmat.com/rates-and-pr ... 39110.html

Machines X and Y produced identical bottles at different constant rates. Machines X. operating alone of 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.

[Ian Stewart]

Take care to distinguish between:

-'simultaneous' rates problems, in which workers work together, at the same time. For such problems, to work out the combined rate of work, you can use either the method you linked to above, or the combined rates formula (mathematically, the two approaches are identical, though I prefer to avoid unnecessary formulas). That's not what's happening in the above question;

-'sequential' rates problems, where workers work in sequence (when one worker stops, the next starts). That is what's happening in the above question.

Back to the question - notice that we don't need to know how quickly X and Y would complete the job if they worked together here, so the conventional combined rates formula won't give us useful information.

Statement 1 is clearly insufficient, since it gives no information about Y.

Statement 2 will be sufficient, since it gives us a comparison of X and Y's rates. We know: the amount of work Y did in 3 hours was half what X did in 4 hours. In other words, if X worked for 2 hours, X would do the same work that Y did in 3 hours. Since we know that 4 hours of X and 3 hours of Y is enough to finish the job, and 3 hours of Y is equivalent to 2 hours of X, then X working alone would take 6 hours to do the job.

[navalpike]

You are awesome. Many thanks as always.

[cubicle_bound_misfit]

taking cue from Ian (who taught me so many things that if charged one dime per lesson it would buy him a 760Li by now ), I am trying to enlist types
of time-work problems that comes in Gmat. Please help me if I miss anything.

1. Comparison between independent efficiency like the problem above

2. Solution of equation(s) for persons working together where each persons rate may or may not be known.

3. work amount constant problems.

like 3 men 30 days 50 bottles
x men 20 days 60 botles etc.

Is there any other type you can think of?

[mitaliisrani]

Take care to distinguish between:

-'simultaneous' rates problems, in which workers work together, at the same time. For such problems, to work out the combined rate of work, you can use either the method you linked to above, or the combined rates formula (mathematically, the two approaches are identical, though I prefer to avoid unnecessary formulas). That's not what's happening in the above question;

-'sequential' rates problems, where workers work in sequence (when one worker stops, the next starts). That is what's happening in the above question.

Back to the question - notice that we don't need to know how quickly X and Y would complete the job if they worked together here, so the conventional combined rates formula won't give us useful information.

Statement 1 is clearly insufficient, since it gives no information about Y.

Statement 2 will be sufficient, since it gives us a comparison of X and Y's rates. We know: the amount of work Y did in 3 hours was half what X did in 4 hours. In other words, if X worked for 2 hours, X would do the same work that Y did in 3 hours. Since we know that 4 hours of X and 3 hours of Y is enough to finish the job, and 3 hours of Y is equivalent to 2 hours of X, then X working alone would take 6 hours to do the job.

Dude thanksss....what a logical way of doing the sum...!!!!...i hated the explanation in the book..u made it so simple