Word Translations - Ratios Solutions PS #14

[ray]

I don't agree with the answer given in the book (for Question 14 of the Ratio Solutions problem in the Word Translations Manhattan GMAT guide).

The question is as follows:

It takes the average dryer 80 minutes to dry one full load of Bob's laundry. Bob has one average dryer and also decides to try one "Super Jumbo-Tron Dryer-Matic", which is faster than the average dryer by a ratio of 5:4. Bob has three loads of laundry, and both machines are so precise that he can set them to the minute. How many minutes does it take for him to dry his three loads (assuming no time passes between loads and he can split them up between dryers)?

The first step in the answering the problem I agree with-- we figure out that it takes 64 minutes for the super dryer to finish one load.

However, the next step in the solution is to assume that we'd put 2 loads in the super dryer-- with which I disagree.

The suggested answer is therefore 128 minutes (since Bob would put 2 loads into the super dryer and one load into an average dryer).

From the previous chapters on rates and work, I thought through the problem by making up a rate chart (since the question says that both machines are so precise that Bob can set them to the minute, that no time passes between loads and that he can split up the loads between dryers).

Average Dryer Super Dryer
Rate 1/80 1/64
Time t t
Work w 3-w

I eventually end up with t=107 minutes and that we'd put in 5/3 load into the super dryer and 4/3 load into the average dryer.

I spent 10 minutes of my tutoring session last night discussing this problem and I don't think we ever came up with a good concensus.

My tutor basically said that you can *only* put whole number loads into the dryers-- but that seems to contradict some of the information given in the question. He also told me that drying out 1/3 of a load of laundry would take as much time as drying a full load-- another point with which I disagree.

So I'm stubborn and still disagree with the answer explanation.

Can anyone provide me with a good explanation as to why the book's answer might be correct?

Thanks!

[Jeff]

Ray -

Sometimes these implied integer constraints are obvious (you can't cut people in half!), but in other cases less obvious. In any case, integer constraints can be really strong, and are important to watch out for, esp. on DS problems.

I think you have a decent argument here since we all know from practical experience that a clothes dryer does in practice dry smaller loads faster, all else equal. The key take-away here though is to recognize that this was intended to be a completely different problem type than the usual rate/work problem. The point was to spot the critical path in the process and find the best way through the process for a given amount of work.

/Jeff

[StaceyKoprince]

Don't worry too much about it - the test won't make you split hairs like that. It'll be obvious when you are allowed to split integers and when you're not allowed to do so.