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Sari and Ken climb up a mountain. At night, they camp together. On the

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Sari and Ken climb up a mountain. At night, they camp together. On the  [#permalink]

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New post Updated on: 25 May 2015, 07:03
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Question Stats:

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Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?

A. 13:00
B. 13:30
C. 14:00
D. 15:00
E. 15:30

AC A;
Ken has to close a gap of 700 meters, and open a new gap of 50 meters, all at the same combined rate of 150 m/hr. Thus, the total gap is 750 meters, and the time it takes him is 750/150 = 5 hours. If Ken started climbing at 08:00, he will reach the summit five hours later at 13:00.

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Originally posted by reto on 25 May 2015, 07:01.
Last edited by Bunuel on 25 May 2015, 07:03, edited 1 time in total.
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Re: Sari and Ken climb up a mountain. At night, they camp together. On the  [#permalink]

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New post 25 May 2015, 22:42
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reto wrote:
Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?

A. 13:00
B. 13:30
C. 14:00
D. 15:00
E. 15:30

AC A;
Ken has to close a gap of 700 meters, and open a new gap of 50 meters, all at the same combined rate of 150 m/hr. Thus, the total gap is 750 meters, and the time it takes him is 750/150 = 5 hours. If Ken started climbing at 08:00, he will reach the summit five hours later at 13:00.


You can do the question in a few seconds if you understand the concept of relative speed.

Both Sari and Ken climb in the same direction.

Speed of Sari = 700/2 = 350 meters/hr (since she covers 700 meters in 2 hrs)
Speed of Ken = 500 meters/hr

At 8:00, distance between Ken and Sari is 700 meters. Ken needs to cover this and another 50 meters.

Time he will take = Total distance to be covered/Relative Speed = (700 + 50)/(500 - 350) = 5 hrs

Starting from 8:00, in 5 hrs, the time will be 13:00

Answer (A)

For more on relative speed, check: http://www.veritasprep.com/blog/2012/07 ... elatively/
http://www.veritasprep.com/blog/2012/08 ... -speeding/
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Re: Sari and Ken climb up a mountain. At night, they camp together. On the  [#permalink]

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New post 25 May 2015, 09:44
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reto wrote:
Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?

A. 13:00
B. 13:30
C. 14:00
D. 15:00
E. 15:30

AC A;
Ken has to close a gap of 700 meters, and open a new gap of 50 meters, all at the same combined rate of 150 m/hr. Thus, the total gap is 750 meters, and the time it takes him is 750/150 = 5 hours. If Ken started climbing at 08:00, he will reach the summit five hours later at 13:00.


Here distance covered by both are equal - Make the distances equl

Time taken to cover the distance is T
Sari's average speed - 350 mts
Ken covered the distance in summit - 500T
Sari covered distance in entire summit - 700+350T+50

700+350T+50=500T -> 150T=750 -> T = 5 Hours

Note: 50 is added here to make the distance covered by both are equal

Alternate Sol:
Sari Ken
At 08:00 700mts 0mts
At 09:00 1050 500
At 10:00 1400 1000
At 11:00 1750 1500
At 12:00 2100 2000
At 13:00 2450 2500

Please some one post the quick solution.

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Re: Sari and Ken climb up a mountain. At night, they camp together. On the  [#permalink]

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New post 27 May 2015, 03:31
1
reto wrote:
Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?

A. 13:00
B. 13:30
C. 14:00
D. 15:00
E. 15:30



Here's how you can easily solve this question once you represent the given information visually:

Let Ken take x hours to reach the summit.

Image

Sari traveled 700 m from 6 AM to 8 AM. So, his speed = 350 m/ hr

So, distance traveled by Sari in x hours = 350x meters

Distance traveled by Ken in x hours = 500x meters

From the image, it's clear that

500x = 700 + 350x + 50

This gives, 150x = 750

That is, x = 5 hours

So, Ken reaches the summit at 8 AM + 5 hours = 2 pm

As you can see, visualization of the given information is the key to solving Time-Speed-Distance questions easily :)

Best Regards

Japinder
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Re: Sari and Ken climb up a mountain. At night, they camp together. On the  [#permalink]

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New post 23 Sep 2017, 13:19
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Re: Sari and Ken climb up a mountain. At night, they camp together. On the &nbs [#permalink] 23 Sep 2017, 13:19
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