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Neel and Jacob start from opposite ends of a 28-mile trail and begin
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09 Feb 2022, 06:15
09 Feb 2022, 06:15
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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
A. 10
B. 12
C. 14
D. 16
E. 18
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Re: Neel and Jacob start from opposite ends of a 28-mile trail and begin
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09 Feb 2022, 08:32
09 Feb 2022, 08:32
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Bunuel wrote:
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
A. 10
B. 12
C. 14
D. 16
E. 18
Let's start by writing a word equation.
When the two travelers meet, they will have both hiked for the same amount of time.
So, we can write: Neel's travel time = Jacob's travel time
Let d = the number of miles Neel traveled
So, 28 - d = the number of miles Jacob traveled (since the sum of their distances must be 28)
Time = distance/rate, so we can plug our values into the word equation to get: d/4 = (28 - d)/3
Multiply both sides of the equation by 12 to get: 3d = 112 - 4d
Add 4d to both sides: 7d = 112
Solve: d = 112/7 = 16
Answer: D
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Re: Neel and Jacob start from opposite ends of a 28-mile trail and begin
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09 Feb 2022, 15:20
09 Feb 2022, 15:20
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BrentGMATPrepNow wrote:
Bunuel wrote:
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
A. 10
B. 12
C. 14
D. 16
E. 18
Let's start by writing a word equation.
When the two travelers meet, they will have both hiked for the same amount of time.
So, we can write: Neel's travel time = Jacob's travel time
Let d = the number of miles Neel traveled
So, 28 - d = the number of miles Jacob traveled (since the sum of their distances must be 28)
Time = distance/rate, so we can plug our values into the word equation to get: d/4 = (28 - d)/3
Multiply both sides of the equation by 12 to get: 3d = 112 - 4d
Add 4d to both sides: 7d = 112
Solve: d = 112/7 = 16
Answer: D
Actually we didn't have to do so much, since they travel for the same amount of time from starting till meeting, the distances travelled by them would be in the ratio of their speeds.
Distance covered by Neil
= \(\frac{4}{(4+3)}*28\)
= \(\frac{4}{7}*28\)
= \(4*4\)
= \(16\)
Hence, option D.
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