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

Question

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

A. 2

B. 10

C. 15

D. 20

E. 40

aarushi1710 · Answer

Total distance covered = 40 miles
Let S1 be the speed of the first half of distance covered (i.e. first 20 miles)

S1 =  \frac{D}{T}  =  \frac{20}{T}

Let S2 be the speed during the second half of the distance covered (i.e. the last 20 miles). We also know that S2 =  \frac{1}{2}  (S1)

Therefore, S2 =  \frac{1}{2}  *  \frac{20}{T}

We also know that second half takes him 10 hours longer than the first half, i.e. it takes him T+10 hours. Thus,

S2 =  \frac{D}{(T+10)}  (Substituting the value of S2)

\frac{1}{2}  *  \frac{20}{T}  =  \frac{20}{(T+10)}

Solving for T, T = 10

It took T+10 hours for Pheidippides to run the second half, i.e. 10+10 = 20 hours

Answer choice (D)

stne · Answer

It is given that Pheidippides runs  40  miles at a constant speed. Let that constant speed be s.

Hence  40   miles must be half the distance. Time taken for this half :  \frac{40}{s}

Second half : Distance  40   and speed  \frac{s}{2 }.  Time taken for second half =  \frac{40 *2}{s }

We know second half took  10  hrs. longer than the first:

\frac{40 *2}{s }  =  \frac{40}{s}+10

Solving for s we get  s=4 , hence the speed for second half is  \frac{s}{2}=2

Hence time taken for second half =  \frac{80}{4}=20

Ans D

Hope it's clear.

ThatDudeKnows · Answer

Well, it certainly can't be A or B! We are left with three answer choices. Let's just Plug In The Answers (PITA). Since we only have three, we start with the middle of those.

D:
It took 20 hours to do the second half. That's 20 miles. He ran 1 mile per hour.
It took 10 hours to do the first half. That's 20 miles. He ran 2 miles per hour. 
Was the second half speed half the previous speed? Yes.

Answer choice D.

ThatDudeKnowsPITA

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards