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.