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# Neel and Jacob start from opposite ends of a 28-mile trail and begin

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Math Expert
Joined: 02 Sep 2009
Posts: 59124
Neel and Jacob start from opposite ends of a 28-mile trail and begin  [#permalink]

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14 Feb 2018, 23:08
2
3
00:00

Difficulty:

5% (low)

Question Stats:

87% (01:07) correct 13% (02:05) wrong based on 100 sessions

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Neel and Jacob start from opposite ends of a 28-mile trail and begin hiking toward each other at the same time. If Neel hikes at a constant 4 miles per hour and Jacob hikes at a constant 3 miles per hour, how many miles will Neel have traveled when he meets Jacob?

A. 10
B. 12
C. 14
D. 16
E. 18

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Concentration: Finance, Accounting
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Re: Neel and Jacob start from opposite ends of a 28-mile trail and begin  [#permalink]

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14 Feb 2018, 23:39
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1
Speed of Neel= 4 miles per hour
Speed of Jacob= 3 miles per hour

Relative speed= 4+3= 7 miles per hour

Time taken by both of them to meet= $$\frac{28}{7}$$= 4 hour.

Distance traveled by Neel in 4 hours= 4*4 = 16 miles

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Re: Neel and Jacob start from opposite ends of a 28-mile trail and begin  [#permalink]

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14 Feb 2018, 23:59
2
An alternate approach to quickly come to conclusion

In these kind of problems where 2 people starts moving towards each other and when they meet, the first thing comes to mind is halfway, that is 28/2 = 14 miles. Lets evaluate whether this one works.

1. Halfway is 14 miles which means Neel would take 3.5 hours to reach halfway mark and at the same time Jacob would have reached only 11.5 miles. So its safe to assume that they meet somewhere more than 3.5 after start i.e Neel would have travelled more than 14 miles. The difference between their location is 3.5 miles.

We can rule out option , A, B and C

2. We already knew that when neel reached 14 miles ,the difference between Neel and jacob is 3.5 miles which is half of the relative speed of Neel and Jacob, which both would cover in 30 mins.

so 3.5 + 0.5 = 4 hours. Neel and Jacob would meet at 4 hours after they start at which point Neel would have traveled 16 miles.

And: D

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Re: Neel and Jacob start from opposite ends of a 28-mile trail and begin  [#permalink]

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23 Jul 2019, 23:33
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Re: Neel and Jacob start from opposite ends of a 28-mile trail and begin   [#permalink] 23 Jul 2019, 23:33
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