Question

a train travels the first 15 km at a uniform speed of 30 km/h and next 75 km at a uniform speed of 50 km/h and the last 10 km at a uniform speed of 20 km/h. calculate the average speed

Answer 1

t1 = 15/30 = 1/2 hr
t2 = 75/50 = 3/2 hr
t3 = 10/20 = 1/2 hr

total time = 1/2+3/2+1/2 = 5/2 hr
total distance = 15+75+10 = 100km

average speed = total distance / total time = 100/(5/2) = 200/5 = 40 km/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