The question ask if Runner A ran a mile in 3 min and 59.4secin 1954, and Runner

Question

The question ask if Runner A ran a mile in 3 min and 59.4secin 1954, and Runner B ran the mile in (3:43.13 seconds) in 1999. Ifthe two runners ran in the same race, each running the entire raceat the average speed that they ran in their respective time intheir days. Runner B would have won. By how manymeters? I found the velocity for each runner, but I'm clueless onwhere to go from there. The question ask if Runner A ran a mile in 3 min and 59.4secin 1954, and Runner B ran the mile in (3:43.13 seconds) in 1999. Ifthe two runners ran in the same race, each running the entire raceat the average speed that they ran in their respective time intheir days. Runner B would have won. By how manymeters? I found the velocity for each runner, but I'm clueless onwhere to go from there.

Explanation / Answer

Convert all to seconds:   A = 239.4 seconds , B =223.13 seconds.   The english statute mile = 5280 ft =1609.3 meters. so lets find the speed of each runner:   A = 1609.3/ 239.4 = 6.72 m/s ;    B = 1609.3 / 223.13 =7.21 m/s. Use proportion now:      6.72 /7.21 = d / 1609.3 . d, will be the distancerunner A will cover as runner B finishes the run, at1609.3 meters.                                     d= 1499.93 meters. Thus,               1609.30m - 1499.93 = 109.3 meters . Then runner B will win by 109.37 meters over runner A. Check: 239.4 - 223.13 = 16.27 seconds, runner a isbehind runner B at finish. Moving at 6.72 m/s times 16.27second equals 109.3 meters

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