Question

A train travels the first 15 km at a uniform speed of 30 km are the next 75 km at a uniform speed of 50 km per hour and the last 10 km at a uniform speed of 20 km per hour calculate the average speed for the train journey

Answer 1

40 km\h
d1=15km s1=30km\h
d2=10km s2=20km\h
d3=75km s3=50km\h

total time taken=t1+t2+t3
=0.5+0.5+1.5=2.5
speed =distance\time
100\2.5=40km\h

Answer 2

Here is your solution

Given :-

First 15 km at a uniform speed of 30km/h.

Next 75km at at a uniform speed of 50km/h.

Last 10km/h at a uniform speed of 20km/h.

Time 1st = distance /speed = 15/30
Time 2nd = distance /speed = 75/50
Time 3rd = distance /speed = 10/20

$total \: time = \frac{15}{30} + \frac{75}{50} + \frac{10}{20} \\ \\ total \: time= \frac{150 + 450 + 150}{300} \\ \\ total \: time \: = \frac{750}{300} = \frac{5}{2}$
Total distance = 15km+75km+10km = 100km

$average \: speed = \frac{total \: distance}{total \: time} \\ average \: speed = \frac{100}{ \frac{5}{2} } = \frac{100 \times 2}{5}\\average \: speed = 40km/h$

Hence,
Average speed of train is 40km/h

Hope it helps you