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John takes 20 min to walk every km. David takes 16 min to walk

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John takes 20 min to walk every km. David takes 16 min to walk  [#permalink]

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20 Mar 2018, 09:55
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Difficulty:

65% (hard)

Question Stats:

69% (02:39) correct 31% (02:57) wrong based on 63 sessions

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John takes 20 min to walk every kilometer (km). David takes 16 min to walk every km. Both of them walk in a race. If David beat John by 240 meters (m), find the length of the race (in km)? (1 km = 1000 m)
A) 1
B) 1.2
C) 1.4
D) 1.5
E) 1.6

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Re: John takes 20 min to walk every km. David takes 16 min to walk  [#permalink]

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20 Mar 2018, 10:26
1
souvonik2k wrote:
John takes 20 min to walk every kilometer (km). David takes 16 min to walk every km. Both of them walk in a race. If David beat John by 240 meters (m), find the length of the race (in km)? (1 km = 1000 m)
A) 1
B) 1.2
C) 1.4
D) 1.5
E) 1.6

Speed of David is 1/16 km per min and speed of John is 1/20 km per min.

In the time it took David to complete d km ( which is what we want to find John could cover only (d - .24) km

What is constant between John and David is the time t.

dist = speed * time
d = t/16 ( for David)
d' = t/20 ( for John)

d - d' = .24km as given...

So d - 16d/20 = 0.24
d ( 4/20) = 0.24
d = 0.24 * 5 = 1.2km

Hence Option B.

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John takes 20 min to walk every km. David takes 16 min to walk  [#permalink]

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20 Mar 2018, 10:29
souvonik2k wrote:
John takes 20 min to walk every kilometer (km). David takes 16 min to walk every km. Both of them walk in a race. If David beat John by 240 meters (m), find the length of the race (in km)? (1 km = 1000 m)
A) 1
B) 1.2
C) 1.4
D) 1.5
E) 1.6

J's rate=1/20 kmpm
D's rate=1/16 kmpm
D gains 1/80 kmpm, or 12.5 mpm, on J
240 meters/12.5 mpm=19.2 minutes
19.2 minutes*1/16 kmpm=1.2 km
B
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Re: John takes 20 min to walk every km. David takes 16 min to walk  [#permalink]

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20 Mar 2018, 10:36
gracie wrote:
souvonik2k wrote:
John takes 20 min to walk every kilometer (km). David takes 16 min to walk every km. Both of them walk in a race. If David beat John by 240 meters (m), find the length of the race (in km)? (1 km = 1000 m)
A) 1
B) 1.2
C) 1.4
D) 1.5
E) 1.6

J's rate=1/20 kmpm
D's rate=1/16 kmpm
D gains 1/80 kmpm, or 12.5 mpm, on J
240 meters/12.5 mpm=19.2 minutes
19.2 minutes*1/16 kmpm=1.2 km
B

I think the math we need to do ( numerical computations) are unnecessarily hard on the method you have proposed.

19.2 min * 1/16 kmpm could take quite a while to solve in exam pressure.

Best,
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“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

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Joined: 15 Nov 2017
Posts: 115
Location: India
Concentration: Operations, Marketing
GPA: 4
WE: Operations (Retail)
John takes 20 min to walk every km. David takes 16 min to walk  [#permalink]

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20 Mar 2018, 10:47
souvonik2k wrote:
John takes 20 min to walk every kilometer (km). David takes 16 min to walk every km. Both of them walk in a race. If David beat John by 240 meters (m), find the length of the race (in km)? (1 km = 1000 m)
A) 1
B) 1.2
C) 1.4
D) 1.5
E) 1.6

Relative Speed diff. = (1/16 - 1/20)mpm
= 4/(20*16) mpm (dont solve it now)
To walk 240 meters, time taken = 240*20*16/1000*4
Length of race(km) = (1/16)*(240*20*16/1000*4) (most of the factors cancels out)
= 1.2 km
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Joined: 28 Dec 2017
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John takes 20 min to walk every km. David takes 16 min to walk  [#permalink]

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01 Apr 2018, 15:21
souvonik2k wrote:
John takes 20 min to walk every kilometer (km). David takes 16 min to walk every km. Both of them walk in a race. If David beat John by 240 meters (m), find the length of the race (in km)? (1 km = 1000 m)
A) 1
B) 1.2
C) 1.4
D) 1.5
E) 1.6

My approach is :

John takes 20 min to walk 1000m
David takes 16 min to walk 1000m

let's calculate the distance John walks in 16 min : 16 *1000 / 20 = 800m, this means that John will loose 200m every 1000m which David walks.
Since David won the race by 240m, and given the ratio john's distance lost to David distance walked, we can easily determine total length of the race : 240 * 1000 / 200 = 1200 (1.2km) Answer B

Hope it helps
John takes 20 min to walk every km. David takes 16 min to walk &nbs [#permalink] 01 Apr 2018, 15:21
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