A car covers the first half of the distance between two places at a speed of 40 km/h and second half at 60 km/h . Find the average speed of the car.
The car covers the entire distance that we'll note as x.
We'll split the distance in half, since the car covers the first half at the v1 speed, of 40 km/h, and the other half at the v2 speed, of 60 km/h.
The first half of distance is covered in the time t1, and the other half in the time t2.
We'll write the formula of speed:
v = x/t (1)
v1 = (x/2)/t1
We'll substitute v1:
40 = (x/2)/t1
t1 = x/80 hour
v2 = (x/2)/t2
We'll substitute v2:
60 = (x/2)/t2
t2 = x/120 hour
Now, we'll write the average speed:
av. v = total distance covered/total time taken
av. v = x/(t1+t2)
We'll substitute t1 and t2:
av. v = x/(x/80+x/120)
av. v = 80*120/(80+120)
av. v = 9600/200
av. v = 48 Km/h
The average speed of the car is av. v = 48 Km/h.