BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

rates and circles

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 122
Joined: Mon Dec 15, 2008 12:03 am
Thanked: 2 times

rates and circles

by vkb16 » Wed Sep 30, 2009 3:58 am
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?

(Pie = p)

4P - 1.6
4P + 8.4
4P + 10.4
2P - 1.6
2P - 0.8

OA is B
My qs is, why do we have to involve Pie in the ans?
I got ans as 24 by following the catchup speed method.
For A to catch up, it will take 20/ (3-2) = 20 hrs.
Now for a to pass 12 miles ahead of B, it will take 12/3 = 4 more hours.
Am I missing something?

thanks!
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 472
Joined: Sun Mar 29, 2009 6:54 pm
Thanked: 56 times

by ssmiles08 » Wed Sep 30, 2009 5:57 am
The radius of the circle is 10, so the distance would be the circumference of the circle which is 20pi.

2(t + 10) + 3t - 12 = 20pi

5t + 8 = 20pi

t = 4pi - 1.6

the time for car B is t + 10 since its already been on the road for 10 more hours.

4pi - 1.6 + 10 = 4pi + 8.4 (B)
You got a dream... You gotta protect it. People can't do somethin' themselves, they wanna tell you you can't do it. If you want somethin', go get it. Period.
Top
Master | Next Rank: 500 Posts
Posts: 399
Joined: Wed Apr 15, 2009 3:48 am
Location: india
Thanked: 39 times

by xcusemeplz2009 » Wed Sep 30, 2009 6:09 am
IMO B

in 10 hrs car B will cover 20 miles at a speed of 2mph

tot dis is 20pi miles

when A will start dis left for passing each other is 20pi-20 miles

relative speed is 3+2=5

time taken to cross is (20pi-20)/5=4pi-4

time taken for another 12 miles is 12/5=2.4

tot time= 4pi-4+2.4=4pi-1.6

now we need to add 10 hrs for tot time of B

4pi-1.6+10=4pi+8.4
It does not matter how many times you get knocked down , but how many times you get up
Top
Master | Next Rank: 500 Posts
Posts: 122
Joined: Mon Dec 15, 2008 12:03 am
Thanked: 2 times

by vkb16 » Wed Sep 30, 2009 10:38 pm
thanks a lot guys! I realised my mistake.. I didnt notice that the 2 cars were going in Opposite directions, and hence we have to ADD the rates, not subtract them!

I have to read the qs stem properly I guess!
Top
Master | Next Rank: 500 Posts
Posts: 156
Joined: Sat Jul 19, 2008 6:41 am
Thanked: 8 times

by enniguy » Wed Jan 13, 2010 8:42 pm
I did the same mistake of subtracting both the speeds. Wonder why. Anyways, this method could be faster I guess.

Total Distance = 20pi - 20 (B has already traveled) + 12 (Extra 12 miles from Qn)
= 20pi - 8.

Total Speed = 3 + 2

time = Distance/Speed
= 4pi - 1.6
But B has already traveled for 10 hours, So
4pi+8.4
Top
GMAT Instructor
Posts: 1302
Joined: Mon Oct 19, 2009 2:13 pm
Location: Toronto
Thanked: 539 times
Followed by:164 members
GMAT Score:800

by Testluv » Wed Jan 13, 2010 8:57 pm
I discussed a solution to this question, and provided some tips for multiple object rate problems here:

https://www.beatthegmat.com/hollyyy-diff ... tml#201896
Kaplan Teacher in Toronto
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 57
Joined: Wed Feb 17, 2010 6:15 pm
Location: MD
Thanked: 2 times

by GMAT680 » Sun Mar 07, 2010 10:59 am
here is my approach to solve this problem.

Car B: D(B) = 2(t+10)
Car A: D(A) = 2pi*r - D(B) + 12 = 3t

Substitute Statement one on 2:
2pi*r - 2(t+10) + 12 = 3t
20pi -2t -20 +12 = 3t
20pi -8= 5t
t = 4pi - 8/5
add 10 hours to find time for t(B) = 4pi -(8/5) + 10 = 4pi + 42/5
Hence t(B) = 4pi + 8.4
Top
Post new topic Post Reply
• Page 1 of 1