Question

1. a marathon is 26.2 miles, or 42.2 kilometers. one kilometer has 1000 meters in it. the actual current world record for marathon runs are 2:02:57 (2 hours, 2 minutes, 57 seconds) for a male and 2:15:25 (2 hours, 15 minutes, 25 seconds) for a female. calculate the average speeds of these runs.

Explanation:

Step1: Convert time to seconds

• For male: \(2\) hours \(= 2\times3600 = 7200\) seconds, \(2\) minutes \(=2\times60=120\) seconds. Total time \(t_{male}=7200 + 120+57=7377\) seconds.
• For female: \(2\) hours \(=2\times3600 = 7200\) seconds, \(15\) minutes \(=15\times60 = 900\) seconds. Total time \(t_{female}=7200+900 + 25=8125\) seconds.

Step2: Calculate speed using \(v=\frac{s}{t}\) (where \(s = 42200\) meters)

• Male speed \(v_{male}=\frac{42200}{7377}\approx5.72\) m/s.
• Female speed \(v_{female}=\frac{42200}{8125}\approx5.19\) m/s.

Answer:

The average speed of the male run is approximately \(5.72\) m/s and the average speed of the female run is approximately \(5.19\) m/s.