A Greek warrior named Pheidippides sprints 50 miles from Marathon to Athens at a steady pace. During the journey, he sustains an injury at the halfway point and continues at half his original speed. If the latter half of the journey takes him 12 hours longer than the first half, what is the duration of Pheidippides' run for the second half?

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The total distance he covers is 50 miles. Let S1 represent the speed for the first half of the distance (the initial 25 miles). We can express S1 as

\frac{D}{T}

\frac{25}{T}

. Let S2 denote the speed during the second half of the distance (the final 25 miles). We know that S2 is half of S1, so S2 =

\frac{1}{2}

\frac{25}{T}

. The second half takes him 12 hours…

Comments

WeiJan 19, 2025

Great question!

JaseemOct 24, 2024

Thank for sharing!!!

What this question tests

Your application of distance = rate × time to trains, boats, and commuters, including relative speed.

Mixing units (miles per hour vs. minutes) or averaging speeds — average speed is total distance over total time.