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The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe

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The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe [#permalink]

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The Greek soldier Pheidippides runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run he injures his foot, and continues to run at half his previous speed. If the second half takes him 10 hours longer than the first half, how many hours did it take Pheidippides to run the second half?


A. 2

B. 10

C. 15

D. 20

E. 40
[Reveal] Spoiler: OA
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The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe [#permalink]

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shyind wrote:
The Greek soldier Pheidippides runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run he injures his foot, and continues to run at half his previous speed. If the second half takes him 10 hours longer than the first half, how many hours did it take Pheidippides to run the second half?


A. 2

B. 10

C. 15

D. 20

E. 40


Several ways to answer this. Here's one:

Given: the second half takes him 10 hours longer than the first half

Write this information as a WORD EQUATION:
(Time to complete first 20 miles) + 10 hours = (Time to complete second 20 miles)

let x = speed traveled for first 20 miles
So, x/2 = speed traveled for second 20 miles

Time = distance/speed so, we take our WORD EQUATION and replace values to get:
20/x + 10 = 20/(x/2)
Simplify to get: 20/x + 10 = 40/x
Multiply both sides by x to get: 20 + 10x = 40
Solve to get x = 2
In other words, the speed traveled for first 20 miles = 2 miles per hour

How many hours did it take Pheidippides to run the second half?
Time to complete second 20 miles = 40/x = 40/2 = 20 = D

NOTE: For more information on using WORD EQUATIONS to solve motion questions, see our free video: http://www.gmatprepnow.com/module/gmat- ... /video/913
For extra practice, try this question: http://www.gmatprepnow.com/module/gmat- ... /video/914

Cheers,
Brent
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Re: The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe [#permalink]

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shyind wrote:
The Greek soldier Pheidippides runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run he injures his foot, and continues to run at half his previous speed. If the second half takes him 10 hours longer than the first half, how many hours did it take Pheidippides to run the second half?


A. 2

B. 10

C. 15

D. 20

E. 40


This is also a great candidate for CHECKING THE ANSWER choices.

How many hours did it take Pheidippides to run the second half?

A) 2
Impossible, since the travel time is 10 hours longer for the second half, which means the travel time for the first half = 2 - 10 = -8 hours (?!?)
ELIMINATE A

B) 10
Impossible, since the travel time is 10 hours longer for the second half, which means the travel time for the first half = 10 - 10 = 0 hours (?!?)
ELIMINATE B

C) 15
So, the travel time for the first half = 15 - 10 = 5 hours
This means speed for first half = (20 miles)/(5 hours) = 4 mph
Speed for second half = (20 miles)/(15 hours) = 4/3 mph
The question says that the travel speed for the second leg is HALF the travel speed for the first leg, HOWEVER 4/3mph is NOT half of 4mph
ELIMINATE C

D) 20
So, the travel time for the first half = 20 - 10 = 10 hours
Hmm, I like this already. The first leg takes HALF the time to complete. So, he must have been traveling twice as fast during the first leg. Everything checks out, so D is the correct answer.

To be safe, let's confirm the numbers.
Speed for first half = (20 miles)/(10 hours) = 2 mph
Speed for second half = (20 miles)/(20 hours) = 1 mph
Perfect, the travel speed for the second leg is HALF the travel speed for the first leg, AND 1mph IS half of 4mph
Great!
Answer: D
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Re: The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe [#permalink]

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shyind wrote:
The Greek soldier Pheidippides runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run he injures his foot, and continues to run at half his previous speed. If the second half takes him 10 hours longer than the first half, how many hours did it take Pheidippides to run the second half?


A. 2

B. 10

C. 15

D. 20

E. 40


total=40miles
for the first 1/2 distance i.e 20 miles ...let speed be S and time taken =T
then for another 20 miles speed will be half=S/2 and time will be 10 hrs longer =(T+10)
as distance in both intervals are equal
ST=S/2(T+10)
T=10hrs.

thus for second half he must be taking =T+10==10+10=20hrs

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Re: The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe [#permalink]

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New post 15 Apr 2018, 14:57
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Re: The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe   [#permalink] 15 Apr 2018, 14:57
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The Greek soldier Pheidippides runs the 40 miles from Marathon to Athe

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