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# In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds

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Manager
Joined: 18 Jul 2019
Posts: 54
In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds  [#permalink]

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24 Nov 2019, 11:02
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Difficulty:

75% (hard)

Question Stats:

39% (02:52) correct 61% (03:01) wrong based on 18 sessions

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In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds and C beats D by 40 seconds. If the speed of A is 54 km/hr, by what distance does B beat C?

(A) 360 m
(B) 380 m
(C) 400 m
(D) 380 m
(E) 500 m
Intern
Joined: 15 Nov 2019
Posts: 2
Re: In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds  [#permalink]

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24 Nov 2019, 11:43

A,B,C&D completed the 6000m race with a gap of 20 sec,30 sec, & 40 sec respectively.
Now, Speed of A was 15 mtr/s therefore A took 400 sec to complete the track and B took 400+ 20 sec, similarly C took 450 sec.
With the time, calculate the speed of B and C.
With the speed, calculate the distance of C at T=420 sec(time when B completed the race), which is 5600mtr, therefore the distance between B and C is 6000-5600= 400 mtrs

A,B,C&D completed the 6000m race with a gap of 20 sec,30 sec, & 40 sec respectively.
Now, Speed of A was 15 mtr/s therefore A took 400 sec to complete the track and B took 400+ 20 sec, similarly C took 450 sec.
With the time, calculate the speed of B and C.
With the speed, calculate the distance of C at T=420 sec(time when B completed the race), which is 5600mtr, therefore the distance between B and C is 6000-5600= 400 mtrs
Manager
Joined: 09 Nov 2015
Posts: 154
Re: In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds  [#permalink]

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25 Nov 2019, 23:42
A's speed = 54 kph = 15 m/s. The time taken by him is 6000/15=400 seconds.
B's time: 400+20=420 seconds
D's time: 420+70=490 seconds
C's time: 490-40=450 seconds

Let VA, VB and VC be the speeds of A.B and C respectively.
THE RATIO OF THE SPEEDS OF TWO MOVING OBJECTS IS EQUAL TO THE INVERSE OF THE RATIOS OF THE TIME TAKEN BY EACH TO COVER THE SAME DISTANCE. Therefore:
VA/VB=420/400.....(i)
VB/VC=450/420.....(ii)
Multiplying (i) and (ii):
VA/VC=450/400....> 15/VC=9/8....> VC=40/3 m/s
So, when B finishes the race, C is 450-420=30 seconds or 30*(40/3)= 400 meters behind. ANS: C
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9871
Location: Pune, India
Re: In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds  [#permalink]

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26 Nov 2019, 05:59
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1
CaptainLevi wrote:
In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds and C beats D by 40 seconds. If the speed of A is 54 km/hr, by what distance does B beat C?

(A) 360 m
(B) 380 m
(C) 400 m
(D) 380 m
(E) 500 m

We are given the speed of A only.
Time taken by A to complete the race= Distance/Speed = 6 km / 54 km/hr = (1/9)*3600 sec = 400 sec
Time taken by B to complete the race is 20 sec extra because A beats B by 20 sec. So time taken by B = 420 sec
Time taken by D to complete the race is another 70 secs so D takes 490 secs
Time taken by C to complete the race is 40 secs less than D (because C beats D by 40 secs) = 450 secs

When distance travelled is same, time taken by B : time taken by C = 420 : 450 = 14:15
When time taken is same, distance travelled by B : Distance travelled by C = 15 : 14
The distance of 15 travelled by B is actually 6 km i.e. 6000 m. This means our multiplier is 400. So the difference of 1 between the distances they travelled is 400.

For more on ratios, check: https://www.veritasprep.com/blog/2011/0 ... of-ratios/
_________________
Karishma
Veritas Prep GMAT Instructor

Re: In a 6 km long race, A beats B by 20 seconds, B beats D by 70 seconds   [#permalink] 26 Nov 2019, 05:59
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