A racing car, in a qualifying two-lap heat, covers the first lap with an average speed of 90 mi/h The driver wants to speed up during the second lap so that the average speed of the two laps together will be 180 mi/h. Show that it cannot be done.

Given:

Average speed of the racing car till 1^st lap s₁ = 90 mi/ h .
Average speed of the racing car till 2^nd lap s₂ = 180 mi/ h
The average speed of the racing car is given as:

Let us assume that the distance traveled by the racing car in one lap in time t is x .
Therefore the average speed ( say s₁)of the racing car in the first lap is given as:


Substituting the given value of s₁ , we calculate the time taken by the racing car to travel a distance x as:


Let us assume that the time taken by the racing car to travel the distance 2x to attain the average speed of 180 mi /h be t¹.
Therefore the average speed (say s2)of the racing car till the second lap is given as:


Substituting the given value of s₂, we calculate the time taken by the racing car to travel a distance 2x to attain the average speed of 180 mi/h as:



Therefore we find that if the racing car want to attain the average speed of 180 mi/h till the second lap, the time in which it must complete the two laps is t’. However as calculated above, with the average speed of 90 mi/ h, the car has already consumed that much time and just managed to complete one lap.
Mathematically,
t’ = t
Therefore it is not possible for the racing car to attain the average speed of 180 mi/ h by the end second lap.