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The car travels half the distance by 20 m/s and the other half of the distance by 30 m/s .
Let the total distance be 2 x such that the half distance is x .
Let the total time taken be T .
Let the time taken for the first distance be t1 and the second distance be t2 .
So we can write that T = t1 + t2 because the total time taken is the sum of the time taken for the first half and the time taken for the second half .
Let the average speed be S .
Speed = distance / time
⇒ time = distance / speed
For the first distance
t1 = x / ( 20 )
⇒ t1 = x / 20
For the second distance
t2 = x / ( 30 )
⇒ t2 = x / 30
For the whole distance
T = 2 x / S
Adding t1 + t2 gives T
T = t1 + t2
⇒ T = x / 20 + x / 30
⇒ 2 x / S = x ( 1/20 + 1/30 )
⇒ 2 / S = ( 1/20 + 1/30 )
⇒ 2 / S = ( 3 + 2 ) / 60
⇒ 2 / S = 5 / 60
⇒ 2 / S = 1 / 12
⇒ S = 12 × 2
⇒ S = 24
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