Question

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

Answer 1

d1-15km
s1-30km/hr
t1-d1/s1-15/30-1/2-0.5hr

d2-75
s2-50
t1-d1/s2-75/50-15/10-1.5hr

d3-10km
s3-20km/hr
t3-d3/s3-10/20-1/2-0.5hr

total distance=15+75+20=110km
total time=0.5+1.5+0.5=2.5hr
AVG speed=total distance/total time
=110/2.5
=11/25

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