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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