circular track

[jain2016]

Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

A) 4pie - 1.6

B) 4pie + 8.4

C) 4pie + 10.4

D) 2pie - 1.6

E) 2pie - 0.8

OAB

[MartyMurray]

Given that the radius of the track is 10, the circumference, which is the length of the track, is 2Ï€r = 2Ï€ x 10 = 20Ï€.

When B goes 2 mph for 10 hours, car B goes 20 miles.

Then A starts going 3 mph.

At that point they are headed toward each other at a rate of 2mph + 3mph = 5mph and they have to cover 20Ï€ - 20 + 12 miles.

To determined the number of hours for which the cars will travel simultaneously, divide the total distance they will travel by their combined rate.

(20Ï€ - 20 + 12)/5 = (20Ï€ - 8)/5 = 4Ï€ - 1.6

B has already traveled for 10 hours. So B will have traveled for a total of 4Ï€ + 8.4 hours.

The correct answer is B.

[GMATGuruNY]

Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?
a) 4Ï€ - 1.6
b) 4Ï€ + 8.4
c) 4Ï€ + 10.4
d) 2Ï€ - 1.6
e) 2Ï€ - 0.8

π ≈ 3.

Car B is traveling for more than 10 hours, so answer choices D and E are too small, and A is unlikely. The correct answer is either B or C.

Circumference of track = 20π ≈ 60 miles.
In 10 hours, distance for B = 2*10 = 20 miles.
60-20 = 40 miles between A and B.
A and B now have to travel the 40 miles between them and then -- after they meet -- keep traveling in opposite directions until there is another 12 miles between them. So the total distance that they need to travel is 40+12 = 52 miles.
When things work together, we can add their rates. Combined rate for A+B = 3+2 = 5 miles/hour.
Time for A+B = Distance/Rate = 52/5 = 10.4 hours.
Since B traveled for 10 hours before A joined in, the total time for B = 10 + 10.4 = 20.4 hours.
Only answer choice B works: 4π + 8.4 ≈ 12 + 8.4 = 20.4.

The correct answer is B

[Brent@GMATPrepNow]

Here's an easier question dealing with people on a circular track: https://www.beatthegmat.com/frank-and-ed ... 29750.html

Cheers,
Brent

[jain2016]

(20Ï€ - 20 + 12)/5 = (20Ï€ - 8)/5 = 4Ï€ - 1.6

B has already traveled for 10 hours. So B will have traveled for a total of 4Ï€ + 8.4 hours.

Hi Marty ,

I understood that we get 4Ï€ - 1.6, but how come 4Ï€ + 8.4 hours ?

Please explain.

Thanks,

SJ

[MartyMurray]

(20Ï€ - 20 + 12)/5 = (20Ï€ - 8)/5 = 4Ï€ - 1.6

B has already traveled for 10 hours. So B will have traveled for a total of 4Ï€ + 8.4 hours.

Hi Marty ,

I understood that we get 4Ï€ - 1.6, but how come 4Ï€ + 8.4 hours ?

Please explain.

Thanks,

SJ

The cars travel together for 4Ï€ - 1.6 hours.

So while A is traveling, B travels for 4Ï€ - 1.6 hours.

B has already traveled for 10 hours by the time A starts traveling. So to get the total time B travels, we need to add the 10 hours of B traveling alone to the 4Ï€ - 1.6 hours of B traveling while A travels.

4Ï€ - 1.6 + 10 = 4Ï€ + 8.4