hongwang9703 wrote:will i see questions like this one regularly on the reall 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?
4PIE-1.6
4PIE+ 8.4
4pie + 10.4
2PIE - 1.6
2pie - 0.8
Hi hongwang,
Both cars are travelling the circumference of a circle. The circumference of this cirlce is 2 * pi* 10 = 20pi miles.
But Car B travels for 10 hours before Car A moves. Because we are going to need to determine where on the circle the cars will meet, we need to determine where on the circle Car B will be after travelling for 10 hours.
Car B's speed is 2 mph, and it is travelling for 10 hours. Using the speed = distance/time formula, this means, Car B has travelled a distance of: 2*10 = 20 miles.
Now, in order to meet, Cars A and B have to mutually close the distance between them. They both begin at the same point somewhere on the circumference (let's call it "origin") but move in opposite directions. Car B has now driven some distance on the circumference. The distance that car B had yet to close before arriving at origin is the distance between the two cars that the two cars will now begin closing (the moment car A moves). Because car B has travelled 20 miles, there are now 20pi - 20 miles (or 20(pi - 1) miles betwen them the moment Car A begins moving. This is the distance both cars will now mutually close.
When two objects are heading towards each other they are approaching each other at a rate that is the sum of their speeds. So they are approaching each other at 5mph. And they are mutually closing a distance of 20pi-20 miles.
Again, using the speed formula, we can compute how long it will take them to meet up:
time to meet = 20(pi -1)/5 = 4 (pi -1) = 4pi -4
At the time they meet, car B has travelled 10 hours alone, and then 4pi-4 hours to meet car A.
Now, they are separating from each other a distance of 12 miles. The rate at which the two cars are separating is, again, the sum of their speeds. So:
time elapsed for them to separate 12 miles = 12/5 = 2.4
Therefore, the total time B has travelled is: 10 + (4pi - 4) +2.4 = 4pi + 8.4, and choose answer choice B
Will you regularly see this kind of question on the GMAT? 100% NO.
COULD you see this question on the GMAT? Possibly. Two object problems are common but, in all of these kinds of problems I've seen, the objects are moving linearly not circularly.
(Tip: When objects are moving in opposite directions (towards each other or away from each other), add their rates. If one object is catching up to another, then subtract their rates.)
But GMAT does love its circles, and so they could ask this question. I don't think I've ever seen an official GMAT question like this, however. Also, the problem seems far too computationally tedious for the GMAT.
