What is the average speed of a train that travells between two places. 3/4 of distance is covered at speed of 80 km / h and 1/4 at 160 km / h

The train travels between 2 places, covering the distance
that we'll note as x.

We'll split the x distance in
3/4, since the train covers the first 3/4 of x at the v1 speed, of 80 km/h, and the
other 1/4 at the v2 speed, of 160 km/h.

The 3/4 of x
distance is covered in the time t1, and the other 1/4, in the time
t2.

We'll write the formula of
speed:

v = x/t (1)

v1 =
(3x/4)/t1

We'll substitute
v1:

80 = (3x/4)/t1

320t1
= 3x

t1 =
3x/320 hour

v2 =
(x/4)/t2

We'll substitute
v2:

160 = (x/4)/t2

t2 = x/640
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/(3x/320+x/640)

av. v =
640/7

av. v = 92
Km/h

The average speed of the train is av. v
= 92 Km/h.