Question regarding rates & work strategy

[shweezy]

Hi all,

Page 29 of the MGMAT WT guide (2007 Edition) has an example at the top that reads as follows:

Stacy and Heather are 20 miles apart and walk toward each other along the same route. Stacy walks at a constant rate that is 1 mph faster than Heather's constant rate of 5mph. If Heather starts her journey 24 minutes after Stacy, how far from her original destination has Heather walked when the two meet?

My question is regarding setting up the R=TD formula for Stacy and Heather. The way the book solves for it is to set up the equations as follows:

Stacey Heather
R 6 5
T t+.4 t
D 20-d d

However, can I still obtain the right answer if I set things up as follows:

Stacey Heather
R 6 5
T t+.4 t
D d 20-d

If not, why?

Thanks!

[StaceyKoprince]

You absolutely can get the right answer that way. But you open up the possibility that you'll make a careless mistake, so I'd recommend doing it the way the book does it.

Here's why: they ask us for Heather's distance. If we set Heather equal to plain d, then when we solve, we're done - d is the answer. If we set Stacy equal to plain D, though, then we have to do an extra step at the end: 20-d. I absolutely guarantee you that, on a problem of this type, Stacy's distance is also going to be in the answer choices. So if you forget that last step, you'll pick Stacy's distance instead of Heather's... and you'll get the problem wrong.

Moral of the story: always try to set things up so that you're solving for what they asked!

[sonygmat]

You absolutely can get the right answer that way. But you open up the possibility that you'll make a careless mistake, so I'd recommend doing it the way the book does it.

Here's why: they ask us for Heather's distance. If we set Heather equal to plain d, then when we solve, we're done - d is the answer. If we set Stacy equal to plain D, though, then we have to do an extra step at the end: 20-d. I absolutely guarantee you that, on a problem of this type, Stacy's distance is also going to be in the answer choices. So if you forget that last step, you'll pick Stacy's distance instead of Heather's... and you'll get the problem wrong.

Moral of the story: always try to set things up so that you're solving for what they asked!

Stacey, I have a question. From the way I solved the exercise I found that H traveled 8 miles and S 12 miles.

Since it asks how far away from her original destination has H walked, should't the answer be 12 miles? Because when they met she traveled 8 miles but she is still 12 miles short from her original destination.

[sonygmat]

Would any instructor care to elaborate pleaseeee?

[StaceyKoprince]

Ah, I see - yes, there is a little bit of ambiguity in the way the sentence is written. We could read the "her" as referring to Stacy or to Heather. Note though that the "her" in the first half of the sentence is definitely referring to Heather, so you should assume the same pronoun also refers to Heather later.

Still, I think we could re-write this one to make sure there's absolutely no ambiguity. I've already submitted it to our editor. :)