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In a 100m race, Sam beats John by 4 seconds. On the contrary

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In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 16m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?

A. 4 seconds
B. 25 seconds
C. 29 seconds
D. 21 seconds
E. 6.25 seconds
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Oct 2013, 01:08, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: 100 meter race [#permalink]

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New post 02 May 2009, 21:51
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D. 21 second

100/Vj - 100/Vs = 4 ----(1)
100/Vs = 84/Vj = 21 ----(2)
solve these 2 equations , Vj=4

Ts = 100/Vs ----> solve from 1st equation , Ts = 21
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Re: 100 meter race [#permalink]

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different approach .

S and J runs 100 m . Lead = 4 sec

S ( 100 ) gives J ( 84 m ) a lead of 16 m. Both finish at the same time . Lead = 0 sec.

So John had to run this 16m in 4 sec so Speed of John = 16 / 4 = 4 m/sec

John run 100m in = 100 / 4 = 25 sec

Time taken by Sam = 25 - 4 = 21 sec.

Ans D
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Re: 100 meter race [#permalink]

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tkarthi4u wrote:
different approach .

S and J runs 100 m . Lead = 4 sec

S ( 100 ) gives J ( 84 m ) a lead of 16 m. Both finish at the same time . Lead = 0 sec.

So John had to run this 16m in 4 sec so Speed of John = 16 / 4 = 4 m/sec

John run 100m in = 100 / 4 = 25 sec

Time taken by Sam = 25 - 4 = 21 sec.

Ans D


Good Approach. I got D too by solving 2 equations and I took 1 min. Your approach probably saves atleast 30 more secs.
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Re: 100 meter race [#permalink]

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New post 29 Oct 2013, 00:39
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One more approach:

(Distance x time) of Sam = (Distance x time) of John
************************************************

Distance travelled by Sam = 100
Time taken by Sam = t


Distance travelled by John = 100-16 = 84
Time taken by John = t+4


84 (t+4) = 100 (t)

Solving this, t= 21
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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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New post 29 Oct 2013, 01:08
asimov wrote:
In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 16m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?

A. 4 seconds
B. 25 seconds
C. 29 seconds
D. 21 seconds
E. 6.25 seconds


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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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New post 09 Nov 2013, 06:42
In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 16m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?

I tried solving out using formulas but I did it out in my head instead.

If Sam allowed John to start out 16m ahead and they finished the race at the same time, while John lost to Sam in the last race by 4 seconds, this means John runs at 16m a second. If John were to start ahead of Sam by this 16m distance and they finished the race at the same time, John would have completed the race in 25 seconds. However, Sam is faster than John and closes the 4 second, 16 meter gap. Sam would have had to spend less time running than John for them to finish the race at the same time, the four seconds that John needed beat Sam.

D. 21 seconds
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Re: 100 meter race [#permalink]

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New post 31 Dec 2013, 07:42
tkarthi4u wrote:
different approach .

S and J runs 100 m . Lead = 4 sec

S ( 100 ) gives J ( 84 m ) a lead of 16 m. Both finish at the same time . Lead = 0 sec.

So John had to run this 16m in 4 sec so Speed of John = 16 / 4 = 4 m/sec

John run 100m in = 100 / 4 = 25 sec

Time taken by Sam = 25 - 4 = 21 sec.

Ans D


I wouldn't say that he had to run 'those' first 16m in 4 seconds but that in total we would have to run an extra 16m whatever they are in the whole track so that it can account for that 4 extra seconds.

The rest is very good

Cheers!
J :)
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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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I think it's really helpful for questions like this to write out the information you know in word form:

1) Sam runs 100 meters in s seconds.
2) John runs 100 meters in s+4 seconds.
3) John runs 84 meters in s seconds.

From here, it's extremely simple:

100 / (s+4) = 84 / s ;

100s = 84 (s+4)

100s = 84s + 336

16s = 336

s = 21;

Hope it's clear.
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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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Their difference is 4 second but this difference is 0 if john allows Sam to start the race from 16m ahead . that means Jhon was 16m away from finishing line when they started together . so He will cover 16 m in 4 seconds . so his speed =16/4=4 metre / second . so time taken =100/4=25 seconds . so Sam took = 21 seconds .

correct answer = D

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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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New post 10 Oct 2015, 13:00
T=Sam's time
100/(T+4)=John's rate in race 1
84/T=John's rate in race 2
100/(T+4)=84/T
T=21 seconds
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In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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arranging info into rtd chart suggested by mgmat is really helpful.

plug (3) into (2) and you receive Jonh's speed of 4 m/sec. So John takes 25 seconds to make 100 meters and Sam takes 4 secs less = 21.
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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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New post 09 Mar 2016, 18:43
took some time to think about how to solve this one...
so John takes 4 seconds more to run the remaining 16 meters. so 16/4 = 4m/s is the speed of John.
john runs 100 meters in 25 seconds.
we know that sam needs 25-4 =21 seconds.

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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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New post 13 Mar 2016, 03:50
asimov wrote:
In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 16m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?

A. 4 seconds
B. 25 seconds
C. 29 seconds
D. 21 seconds
E. 6.25 seconds


Given: Sam gives John a start of 16 m and they reach at the same time
It implies that when John covers 84 m, Sam covers 100 m in the same time
Therefore, their speed will be in the ratio of 84 to 100 and time taken will be in the ratio of 100 to 84
Reducing the ratio of time we get, 21 to 25 which gives that difference of 4 seconds.
Therefore, the time taken by Sam is 21 seconds.
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Re: In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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Hello from the GMAT Club BumpBot!

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In a 100m race, Sam beats John by 4 seconds. On the contrary [#permalink]

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New post 20 May 2017, 17:40
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asimov wrote:
In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 16m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?

A. 4 seconds
B. 25 seconds
C. 29 seconds
D. 21 seconds
E. 6.25 seconds


Since distance is the same in the first case, first equation is s1/s2=t2/t1
Since time is the same in the second case, second equation is s1/s2= d1/d2
Therefore, d1/d2=t2/t1
84/100=(t-4)/t
t=25,
t-4=21 seconds
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In a 100m race, Sam beats John by 4 seconds. On the contrary   [#permalink] 20 May 2017, 17:40
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