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28 Jun 2022, 04:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (02:30) correct
18%
(02:17)
wrong
based on 76
sessions
History
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Time
Result
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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
A. 2
B. 10
C. 15
D. 20
E. 40
29 Jun 2022, 05:57
Kudos
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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
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Bunuel
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.
