Question

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

Answer 1

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