Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Dec 1310:00 AM EST
-12:00 PM EST
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Dec 1411:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.- Dec 15
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!
28 Jun 2022, 04:45
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
80% (02:31) correct
20%
(02:18)
wrong
based on 59
sessions
History
Date
Time
Result
Not Attempted Yet
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
29 Jun 2022, 05:57
Kudos
Bookmarks
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)
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)
04 Jul 2022, 12:16
Kudos
Bookmarks
Bunuel
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
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.
