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Sari and Ken climb up a mountain. At night, they camp together. On the [#permalink]
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25 May 2015, 06:01
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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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Last edited by Bunuel on 25 May 2015, 06:03, 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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25 May 2015, 08:44
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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+ 50700+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 2500Please some one post the quick solution. Thanks
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Re: Sari and Ken climb up a mountain. At night, they camp together. On the [#permalink]
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25 May 2015, 21:42
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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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27 May 2015, 02:31
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. 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 metersFrom 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 TimeSpeedDistance questions easily Best Regards Japinder
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