Question

A train travels the first 15km at a uniform speed of 30km/h;the next 75km at uniform speed of 50km/h;and the last 10km at a uniform speed of 20km/h.Calculate the average speed for the entire train journey

Answer 1

Given :-

A train travels first 15km at a speed of 30km/h

Next 75km at a speed of 50km/h

Last 10km at a speed of 20km/h

To find:-

We have to find the average speed of whole journey !

$\boxed{\sf \ Average \ speed = \dfrac{Total \ Distance }{Total \ Time }}$

• So , we have to calculate the time

$\sf \ speed = \dfrac{Distance }{Time}\\ \\ \longrightarrow\sf Time_1= \dfrac{Distance_1}{Speed_1}\\ \\ \longrightarrow\sf Time_1= \cancel{\dfrac{15}{30}}\\ \\ \longrightarrow\sf Time_1= \dfrac{1}{2}= 0.5 h$

$\underline{\sf\ \ Time \ taken \ for \ 1st\ part\ of \ journey= 0.5\ h}$

• Now time taken to cover 2nd part of journey

$\sf \ Time_2= \dfrac{Distance_2}{Speed_2}\\ \\ \longrightarrow\sf Time_1= \cancel{\dfrac{75}{50}}\\ \\ \longrightarrow\sf Time_1= \dfrac{3}{2}= 1.5 h$

$\underline{\sf\ \ Time\ taken \ for \ 2nd\ part\ of \ journey= 1.5\ h}$

$\sf \ Time_3= \dfrac{Distance_3}{Speed_3}\\ \\ \longrightarrow\sf Time_1= \cancel{\dfrac{10}{20}}\\ \\ \longrightarrow\sf Time_1= \dfrac{1}{2}= 0.5 h$

$\underline{\sf\ \ Time \ taken \ for \ last\ part\ of \ journey= 0.5\ h}$

Now finally calculate the average speed of train !

$\sf \ Av.\ speed= \dfrac{Total \ distance }{Total \ time}\\ \\ \longrightarrow\sf Av.\ speed= \dfrac{ d_1+d_2+d_3}{t_1+t_2+t_3}\\ \\ \longrightarrow\sf Av.\ speed =\dfrac{15+75+10}{0.5+1.5+0.5}\\ \\ \longrightarrow\sf Av.\ speed = \cancel{\dfrac{100}{2.5}}\\ \\ \longrightarrow\sf Av.\ speed = 40km/h$

$\underline{\sf\ \ Average \ speed \ of \ train = {\boxed{\sf\ \ 40km/h}}}$