akhp77 wrote:Source: MGMAT CAT
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?
A: 4 π - 1.6
B: 4 π + 8.4
C: 4 π + 10.4
D: 2 π - 1.6
E: 2 π - 0.8
OA: B
Hi,
even though this is a circular track problem, we can treat it as if it were a straight line.
First, we know that we're going to apply our basic formula: distance = rate * time
Let's calculate the distance between A and B at the start, i.e. the circumference of the track.
Circumference = 2(pi)r = 20pi
So, let's picture A and B starting at opposite ends of a road that's 20pi miles long.
B starts first at 2mph. After 10 hours, B has travelled 20 miles. So, when A starts moving, the distance between A and B is:
(20pi - 20) miles
Now A and B are both moving, directly towards each other. When two objects move directly towards (or away from) each other, we ADD their rates to get the overall rate.
Accordingly, once A and B are moving, their combined rate is 5 mph.
If the question had asked when does A meet B, we'd use r=5 and d=(20pi-20). However, this question asks about when car A has moved 12 miles past car B. So, the actual distance left to travel is:
(20pi - 20) + 12 = 20pi - 8
Finally, we have everything we need:
d = (20pi - 8)
r = 5
t = d/r = (20pi - 8)/5 = 4pi - 8/5 = 4pi - 1.6
Is 4pi - 1.6 one of the choices?
Of course it is! The GMAT loves to provide answers that are the "right answer to the wrong question". Hence
step 4 of the Kaplan Method for Problem Solving: always confirm that you've answered the right question.
The time we've calculated is the time since A started moving; the question asks for how long B has been moving. Since B started 10 hours before A, we have to add 10 hours:
4pi - 1.6 + 10 = 4pi + 8.4... choose (B).
