Word Problems Strategy Guide: rates and work

[clarence.booth]

Hi,

I'm reviewing a problem in the Word Problems strategy guide (5th. ed.) on pg. 35 which says:

Car X is 40 miles west of Car Y. Both are traveling east and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

In the work shown, the time of 2 hours and 40 mins is shown as 8/3.

How did they arrive at that fractional conversion of 8/3 from 2 hours and 40 minutes?

[StaceyKoprince]

Please remember to read (and follow!) the forum guidelines before posting.

This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). If you are a course student, you can also ask about other problems or issues before or after class or during section.

This particular question would go in the MGMAT non-CAT quant folder. I'll give you a short answer here but, if you want to discuss further, you'll need to post in that other folder. :)

2 hours and 40 minutes
Think of an hour as 1 unit. If you had 1 hour, you could write that as 3/3 (=1). If you had two hours, you could write that as 6/3 (=2).

It gets a little weird when you hit the minutes. There are 60 minute in an hour, so the additional 40 minutes have to be represented in terms of 40/60, which reduces to 2/3.

So you have 6/3 (for two hours) + 2/3 (for 40 minutes) = 8/3.