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by rakeshmeher » Tue Jun 29, 2010 2:06 am
Two marathon runners are training by running on a 24-mile track that forms a circle around a certain city. Both runners begin at the same spot, running in opposite directions around the track. Runner A completes the entire track in 2 hours; runner B completes it in 3 hours. Assuming that both runners ran at a constant speed, for how many miles did runner A run before he met runner B ?
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by sanju09 » Tue Jun 29, 2010 2:20 am
rakeshmeher wrote:Two marathon runners are training by running on a 24-mile track that forms a circle around a certain city. Both runners begin at the same spot, running in opposite directions around the track. Runner A completes the entire track in 2 hours; runner B completes it in 3 hours. Assuming that both runners ran at a constant speed, for how many miles did runner A run before he met runner B ?
Relative motion along circle is NOT tested on GMAT. The nosy can still post the same question on the GMAT Math Forum of BTG to see my take on it.
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by rakeshmeher » Tue Jun 29, 2010 2:37 am
consider it done and take it on then plz............
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by gmatmachoman » Tue Jun 29, 2010 3:10 am
here it goes!!

Sa & Sb be speeds of A&B
Sa=Sb (given)

Tmeet: Time taken by 2 cars to meet

Tmeet = Distance/ Relative speed

=24/(Sa +Sb)
=24/(2Sa)
=12/Sa

Equation 2:

Speed of car * Time taken by car = Distance travelled by car

(Sa * Tmeet )+( Sa * (2-Tmeet)) = 24

Apply Sa in terms of Tmeet:

SO u will get Tmeet = 1hr & Sa=12

Distance travelled : Sa * Tmeet

12*1= 12 miles
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by amising6 » Tue Jun 29, 2010 3:15 am
rakeshmeher wrote:Two marathon runners are training by running on a 24-mile track that forms a circle around a certain city. Both runners begin at the same spot, running in opposite directions around the track. Runner A completes the entire track in 2 hours; runner B completes it in 3 hours. Assuming that both runners ran at a constant speed, for how many miles did runner A run before he met runner B ?
A speed =24/2=12mph
B speed=24/3=8mph
now they are running in opposite direction there relative sped 12+8=20mph
so they will meet after 24/20=1.2 hrs =1hr 12 mins=6/5


so distance tarvelled by A=6/5*12=14.4 miles
so distance tarvelled by B=6/5*8=9.6 miles


so runner Arun will run 14.4 miles before they meet
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by sanju09 » Tue Jun 29, 2010 5:35 am
sanju09 wrote:
rakeshmeher wrote:Two marathon runners are training by running on a 24-mile track that forms a circle around a certain city. Both runners begin at the same spot, running in opposite directions around the track. Runner A completes the entire track in 2 hours; runner B completes it in 3 hours. Assuming that both runners ran at a constant speed, for how many miles did runner A run before he met runner B ?
Relative motion along circle is NOT tested on GMAT. The nosy can still post the same question on the GMAT Math Forum of BTG to see my take on it.
On second look, it seems ok for GMAT to me...


When two bodies move around a circle in opposite direction, the relative speed is taken to be the sum of their individual constant speeds.

Runner A's constant speed = 24/2 = 12 mph

Runner B's constant speed = 24/3 = 8 mph

The relative speed = 12 + 8 = 20 mph.

Hence it would take 24/20 = 1.2 hours when they would first meet on the said track. Meanwhile, the runner A would have travelled [spoiler]12 × 1.2 = 14.4 miles.[/spoiler]
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by sanju09 » Tue Jun 29, 2010 5:37 am
gmatmachoman wrote:here it goes!!

Sa & Sb be speeds of A&B
Sa=Sb (NOT given)

Tmeet: Time taken by 2 cars to meet

Tmeet = Distance/ Relative speed

=24/(Sa +Sb)
=24/(2Sa)
=12/Sa

Equation 2:

Speed of car * Time taken by car = Distance travelled by car

(Sa * Tmeet )+( Sa * (2-Tmeet)) = 24

Apply Sa in terms of Tmeet:

SO u will get Tmeet = 1hr & Sa=12

Distance travelled : Sa * Tmeet

12*1= 12 miles
little complex terminology, young man!
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by sanju09 » Tue Jun 29, 2010 5:39 am
Motion along a circle, in its complex form would never be tested on GMAT, this much could be the limit.
Last edited by sanju09 on Tue Jun 29, 2010 5:41 am, edited 1 time in total.
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by sanju09 » Tue Jun 29, 2010 5:39 am
amising6 wrote:
rakeshmeher wrote:Two marathon runners are training by running on a 24-mile track that forms a circle around a certain city. Both runners begin at the same spot, running in opposite directions around the track. Runner A completes the entire track in 2 hours; runner B completes it in 3 hours. Assuming that both runners ran at a constant speed, for how many miles did runner A run before he met runner B ?
A speed =24/2=12mph
B speed=24/3=8mph
now they are running in opposite direction there relative sped 12+8=20mph
so they will meet after 24/20=1.2 hrs =1hr 12 mins=6/5


so distance tarvelled by A=6/5*12=14.4 miles
so distance tarvelled by B=6/5*8=9.6 miles


so runner Arun will run 14.4 miles before they meet
BINGO! But who's Arun?
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by GMATGuruNY » Tue Jun 29, 2010 6:23 am
rakeshmeher wrote:Two marathon runners are training by running on a 24-mile track that forms a circle around a certain city. Both runners begin at the same spot, running in opposite directions around the track. Runner A completes the entire track in 2 hours; runner B completes it in 3 hours. Assuming that both runners ran at a constant speed, for how many miles did runner A run before he met runner B ?
A and B are running toward each other to cover the 24 miles of the track. So when they meet, their combined distance must be 24 miles.

Since every question on the GMAT is multiple-choice, the easiest approach would be to try each answer choice until you find the one that gives A and B a combined distance of 24 miles.

A's rate is 24/2 = 12 miles/hour.
B's rate is 24/8 = 8 miles/hour.

If we plug in the answer that says A will have covered 14.4 miles:

A's time = 14.4/12 = 1.2 hours
B's distance in 1.2 hours = 8 * 1.2 = 9.6 miles

Since 14.4 + 9.6 = 24 miles, we have found the correct answer. They will meet when A has run 14.4 miles.

Whenever you're stuck, remember that the GMAT is a multiple choice test. The correct answer has to be one of the answer choices. You just need to figure out which one is correct.
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