Three runners A, B and C run a race, with runner A finishing 12m ahead : GMAT Problem Solving (PS)
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Three runners A, B and C run a race, with runner A finishing 12m ahead

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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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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
[Reveal] Spoiler: OA

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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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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.

as speeds are constant, we have equation,

x-12/ x-18 = 12/10 > x = 48.

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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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20 Sep 2011, 02:12
Can someone better explain this?
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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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20 Sep 2011, 02:34
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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?

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.

..._________C___(6)___B_______(12)________A (Finishing Point)

..._____________________C_______(8)______B (Finishing Point)

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
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Forum Moderator Joined: 20 Dec 2010 Posts: 2021 Followers: 161 Kudos [?]: 1703 [0], given: 376 Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink] Show Tags 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) And we know the final lead was 8 meters So, 6L/(L-12)=8 3L/(L-12)=4 3L=4L-48 L=48m Ans: "B" _________________ Manager Status: Do till 740 :) Joined: 13 Jun 2011 Posts: 113 Concentration: Strategy, General Management GMAT 1: 460 Q35 V20 GPA: 3.6 WE: Consulting (Computer Software) Followers: 1 Kudos [?]: 10 [0], given: 19 Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink] Show Tags 13 Oct 2011, 09:53 Karishma, can you pls xplain this part Quote: 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) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2132 Kudos [?]: 13632 [3] , given: 222 Re: Three runners A, B and C run a race, with runner A finishing 12m ahead [#permalink] Show Tags 14 Oct 2011, 06:09 3 This post received KUDOS Expert's post shankar245 wrote: Karishma, can you pls xplain this part Quote: 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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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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31 Oct 2014, 02:02
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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
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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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21 Dec 2016, 02:16
Hello from the GMAT Club BumpBot!

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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
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
Three runners A, B and C run a race, with runner A finishing 12m ahead   [#permalink] 23 Dec 2016, 11:43
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