Question

In order to qualify for the finals in a racing event, a race car must achieve an average speed of 223 km/h on a track with a total length of 1350 m. if a particular car covers the first half of the track at an average speed of 215 km/h, what minimum average speed must it have in the second half of the event in order to qualify? answer in units of km/h.

Answer 1

Total track distance is
d = 1350 m = 1.35 km
Half of the track length is  1.35/2 = 0.675 km

The average speed should be 223 km/h. Therefore the total travel time is
t = (1.35 km)/(223 km/h)
  = 6.054 x 10⁻³ h

Half of the track length is traveled at an average speed of 215 km/h. The time taken is
t₁ = (0.675 km)/(215 km/h)
   = 3.14 x 10⁻³ h

In order to satisfy the average speed requirement, the second half of the track should take no more than
t₂ = t - t₁
   = (6.054 - 3.14) x 10⁻³
   = 2.914 x 10⁻³ h

The minimum average speed required to satisfy this time is
v = (0.675 km)/(2.914 x 10⁻³ h)
   = 231.64 km/h

Answer:
The minimum average speed required is 232 km/h (nearest whole number)