What is the average speed of a truck if it travels 2/3 of a distance between 2 towns at 80 km/h and the remaining distance at 90 km/h?

The distance between towns, covered by the truck is
unknown and we'll note it as x.

We'll split the distance in
2x/3 and x/3, since the truck covers the first part of distance at the v1 speed, of 80
km/h, and the other part at the v2 speed, of 90 km/h.

The
first part 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 =
(2x/3)/t1

We'll substitute
v1:

80 = (2x/3)/t1

We'll
divide by 2:

40 = x/3t1

t1 =
x/120 hour

v2 = (x/3)/t2

We'll
substitute v2:

90 =
(x/3)/t2

t2 = x/270 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/120+x/270)

av. v =
x/(9x+4x)/1080

av. v =
1080x/13x

We'l simplify and we'll
get:

av. v = 1080/13

av. v
= 83 Km/h approx.

The average speed of the
car is av. v = 83 Km/h.