Question

A long distance running is running the 10000 m race. He runs the first 2000 m in 5 minutes, the next 5000 m in 14 minutes and the final 3000 meters in 7 minutes. What was the runner’s average speed?

Answer 1

This kind of problems are solved by dividing total distance with the total time necessary for him to get from the start to the finish line. In this case, total distance is 10000m and the total time is the sum of the times that were given (which is 26 minutes, or 1560 seconds). Dividing these two numbers, the average speed is:
$\frac{1000m}{1560s} = 6.41 \frac{m}{s}$

Answer 2

d=d₁+d₂+d₃

t=t₁+t₂+t₃

v₁=d₁/t₁=2000/300=6.66 m/s

v₂=d₂/t₂=5000/840=5.95 m/s

v₃=d₃/t₃=3000/420=7.14 m/s

t₁=d₁/v₁

t₂=d₂/v₂

t₃=d₃/v₃

vm=d/t=d/(d₁/v₁+d₂/v₂+d₃/v₃)=d/(v₂v₃d₁+v₁v₃d₂+v₁v₂d₃)/v₁v₂v₃=v₁v₂v₃d/(v₂v₃d₁+v₁v₃d₂+v₁v₂d₃)=6.66*5.95*7.14*10000/(5.95*7.14*2000+6.66*7.14*5000+6.66*5.95*3000)=2829367.8/441609=6.406 m/s