John and Al are in a 15 km race John averages 44 ms during t

John and Al are in a 15 km race. John averages 4.4 m/s during the first half of the race and then runs at a speed of 4.2 m/s until the last 200 m, which he covers at 4.5 m/s. At what average speed must Al run to beat John?

Solution

John runs 7500m at 4.4m/s. This takes time = 7500/4.4 = 1704.5s
then
John runs 7300m at 4.2m/s. This takes time = 7300/4.2 = 1738.1s
then
John runs 200m at 4.5m/s. This takes time = 200/4.5 = 44.4s

Total time = 1704.5 + 1738.1 + 44.4 = 3487s

To cover 15000m in 3487s requires an average speed of
15000/3487 = 4.3m/s

So Al must run at 4.3m/s or faster to beat John.