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Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink]

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19 Sep 2011, 08:27

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68% (03:18) correct
32% (02:58) wrong based on 128 sessions

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Three runners A, B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?

Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink]

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19 Sep 2011, 09:34

Let distance of race be x mtrs. Then when A finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.

Three runners A,B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?

A. 36m B. 48m C. 60m D. 72m E. 84m

See if you can logically deduce the answer: This is what happens in the race.

Focus on B and C. B and C had a distance of 6 m between them. When B finished the race by covering another 12 m, he created a gap of 8 m between them i.e. he created another 2 m gap while running 12 m. Since he created a gap of 2 m by running 12 m, he must have created a gap of 8 m by running a total of 12*4 = 48 m
_________________

Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink]

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20 Sep 2011, 02:42

jamifahad wrote:

Three runners A,B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?

A. 36m B. 48m C. 60m D. 72m E. 84m

|---------------------------L-------------------|L=Length of the track |-----------------------------C------B----------|A |------------------------------------|<--12---->| A finishes 12 m ahead of B |-----------------------------|<------18------->| A finishes 18 m ahead of C |-----------------------------|<-6->|---------->| So, B was 6 meters ahead of C when A finished the race ------------1

|----------------------------------------C------|B |----------------------------------------|<-8-->| B finishes 8 meter ahead of C--------------2

From 1 and 2, we can deduce that B ran a distance of "L-12" meters taking a lead of 6 meters on C.

L-12->6 1 meter-> 6/(L-12) {:This is the per meter lead by B on C}

For the entire race of L meters, the lead would be L meters->L*6/(L-12)

Since he created a gap of 2 m by running 12 m, he must have created a gap of 8 m by running a total of 12*4 = 48 m

Im nt able to logically deduce how we got the length of the race?

c ----b -----A(finishes)

Think of the logic this way:

There are 2 people P and Q. They both start running simultaneously at different but uniform speeds. In the time P has covered 2 m, Q has covered only 1 m. What will be the distance between them by the time P covers a total of 4 m? P and Q are running at uniform speeds. Since P created a gap of 1 m in every 2 m he ran, the gap between them must be 2 m now.

Now imagine that P is standing ahead of Q by 6 m. They both start running. What happens by the time P covers 2 m? What is the gap between them? It must be 7 m now since another 1 m gap would have got created.

The logic used here is exactly the same.

B and C had a distance of 6 m between them at one point in time. B covered another 12 m and now the distance between them is 8 m. So basically a gap of 2 m was created by B when he ran 12 m. Overall, at the end of the race, the gap between B and C is 8 m. How much must B have run to create a gap of 8 m ( = 4*2)? He must have run 4*12 = 48 m
_________________

Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink]

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31 Oct 2014, 02:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink]

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06 Nov 2015, 21:54

Let d=distance of race. Between A's finish and B's finish, B runs 12 meters while C runs 10 meters. B's rate to C's rate=6/5. When B finishes, he is 8 meters ahead of C. 6/5=d/(d-8) d=48 meters

Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink]

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21 Dec 2016, 02:16

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink]

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23 Dec 2016, 11:43

jamifahad wrote:

Three runners A, B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?

A. 36m B. 48m C. 60m D. 72m E. 84m

Although solution by karishma is more logical and faster approach i providing one conceptual way for solving...

Let speed of A,B,C be A,B &C respectively & total distance be D

then for the first case when A finishes,, the time run by all three will be same D/A=(D-12)/B && D/A=(D-18)/C or (D-12)/B=(D-18)/C----------(i)

again for second case when B finishes,, time taken by B & C will be same thus D/B=(D-8)/C C={(D-8)*B}/D-------(ii)

putting value of C from (ii) to (i) and solving for D we get D=48

Ans B

gmatclubot

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