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This problem trains for: SAT-I, AMC-8, GMAT.

Using a third generation time machine, a contest is set between Perseus riding Pegasus and Alexander riding Bucephalus. They are set to start at the two ends of a straight road some 10 stadiums apart (FYI: approximately 1.4 miles). Pegasus gallops at 19 stadiums per hour and Bucephalus gallops at 21 stadiums per hour. If they both run at a constant rate from one end of the road to the other what is the difference between the times when they are 5 stadiums apart?

(characters from ancient Greek history and legends)

For the first time, they are 5 stadiums apart when the sum of the distances covered by each during this same time is:

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Denoting this time by t1, the distance covered by Bucephalus is:

equation

while the distance covered by Pegasus is:

equation

Since the two distances must add up to 5 stadiums, we can calculate the time t1:

equation

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The second time around, they are 5 stadiums apart after they have met and continued to run in opposite directions until a certain time t2.

At this time, the sum of the distances covered by each equals the 10 stadiums they covered to the meeting point plus the additional 5 stadiums:

equation

In a similar manner to the one above, we can calculate the time t2:

equation

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The difference between the two times is:

equation

Since the time has been measured in hours, this fraction represents the number of hours. We multiply it by 60 to convert it to minutes. One quarter of an hour is 15 minutes.