pkw209 wrote:From Manhattan GMAT:
Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will car B have been traveling when car A has passed and moved 12 miles beyond car B?
Answer to come...
My first answer to this question is 'who cares?' -- and I'm only part joking; there are a lot of steps thrown into this problem that really only serve to make the calculation tedious and un-GMAT-like, and which only serve to obscure the interesting part of the question, which is what to do with the speeds of two objects moving towards each other -- but we can solve it anyway:
* The circumference of the track is 2*Pi*r = 20*Pi miles. If the answer choices are far enough apart, I'd consider rounding this off to 60 for ease of calculation (posting answer choices would be useful).
* Car B travels for 10 hours before A starts. In that time, B travels 20 miles.
* When A begins moving, B and A are traveling in opposite directions, and the gap between them is closing by 5 miles per hour (A closes the gap on its end by 3 miles each hour, while B closes the gap on its end by 2 miles per hour, so we add their speeds)
* When A starts moving, the distance between A and B is 20*Pi - 20 miles. We want to add 12 to this, since we need A to get 12 miles beyond B. So we need to know how long it will take, at 5 mph, to cover a distance of 20*Pi - 20 + 12 = 20*Pi - 8 miles. Since time = distance/speed, the answer is (20*Pi - 8)/5 = 4*Pi - 1.6.
* Now, that's not quite the answer to the question; that's the time it takes from when A starts moving. We need the time from when B starts moving, so we must add on the 10 hours when B was moving and A was not, to get an answer of 4*Pi + 8.4.
There are a lot of make-work steps in this question (accommodating B's head start, finding the time to meet, accommodating the extra 12 miles, not forgetting to add 10 at the end), more than you would see in a real GMAT question. It's the type of question which you might want to understand how to solve -- in particular, it is helpful to understand why we add the speeds of the two cars when they are moving towards each other -- but where you would not want to be overly concerned if you couldn't do it within two minutes.
