Car B begins moving at 2 mph around a circular track with a radius of

VeritasKarishma if circumference of circle is 20pi doesntt it mean that whole circumference is 20 miles ? And B covered a distance of a one whole circle instead of fraction i.e. 20p-20 ?

Circumference of a circle is 2*pi*r which is the length of the track. Since radius is 10 miles, the length is 2*pi*10 = 20*pi which is something more than 60 miles because pi = 3.1416

B travels at 2 mph for 10 hrs so covers 20 miles. Hence in 10 hrs, of the 60+ miles of the track, B covers only 20 miles.
Now A and B need to cover the rest of 40+ miles together.

The distance left for A to complete one whole lap + twelve extra miles, driven at the cars' combined rate:

(20Pi - 20) + 12 = 5t

(20Pi - 8)/5 = t

Adding the first 10 hrs as fifths gives:

(20Pi + 42)/5 = 4Pi + 8,4

It's fascinating to me that more than 50% of responses have been incorrect. If B has been driving for 10 hours before A even starts and we are asked how long B drives, it MUST be greater than 10.
A. Roughly 12.6-1.6 = 11. C'mon, that's obviously too low. Wrong.
B. Roughly 12.6+8.4 = 21. Okay, hold onto it.
C. Roughly 12.6+10.4 = 23. Okay, hold onto it.
D. Roughly 6.3-1.6 = 4.7. That's not even as long as B drove before A even started!! Wrong.
E. Roughly 6.3-0.8 = 5.5. That's not even as long as B drove before A even started!! Wrong.

At the worst, without doing anything other than using simple logic (and barely any math), we have a 50/50. And yet, more than 50% of people have gotten this question wrong. Missing the logic of the question is a HUGE problem. Please, on difficult problems, save yourself from picking a silly answer just by taking a few seconds to deploy some logic!!



Okay, so now you want to know how to solve this in a way that I haven't seen yet on this thread? I'm going to use two of my favorite techniques on geometry questions: ballparking and manipulating the figure.

First, there's really nothing about this problem that forces it to be a circular track rather than a straight road with two cars driving toward each other. My brain is much better at visualizing the straight road, so I'm going with that (I always look for opportunities to convert circles into straight lines when the circles are used as tracks)!!

The distance between the cars at the beginning is 20pi. Lol @ 20pi. Ballpark! 63 (blue arrow).

B starts driving for 10 hours, so it covers 20 miles (green arrow). That means B and A are now separated by 43 miles (red arrow). We need to close that gap to zero and then keep going until the cars are separated by 12 miles, now with B on the right and A on the left. So, they need to travel 55 miles combined. At a combined rate of 5mph, that's 11 hours on top of the 10 that B already traveled solo. That's a total of 21 hours. Look at the answer choices.

A. Roughly 12.6-1.6 = 11.
B. Roughly 12.6+8.4 = 21.
C. Roughly 12.6+10.4 = 23.
D. Roughly 6.3-1.6 = 4.7.
E. Roughly 6.3-0.8 = 5.5.

Answer choice B.


ThatDudeKnowsBallparking
ThatDudeKnowsGeometry

Hi, I was wondering what did i do wrong here.
I was able to setup a similar equation to this, which is

3T + 2(T+10) = 20pi + 12

Assuming that B travelled 10 hrs more than A.

peaarrr

It appears that you have assigned T to be the amount of time that A travels, but the question asks for how long B travels. Did you remember to add 10 hours to account for "Ten hours later, Car A leaves from the same point in the opposite direction?"

Hi Everyone, just wanted to know if these level of difficult Questions can we really expect for the actual GMAT.