Question

On a 60 km straight road, a bus travels the first 30 km with a uniform speed of 30 kmh-1. How fast must the bus travel the next 30 km so as to have average speed of 40 kmh-1for the entire trip?​

Answer 1

Given :-

Total distance = 60 km

Average speed= 40km/h

Speed for first 30km = 30km/h

To find :-

The speed of train for next 30km

Now first find the time taken by the whole trip

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

$\longrightarrow\sf 40= \dfrac{60}{Total\ Time}\\ \\ \longrightarrow\sf Total \ Time = \cancel{\dfrac{60}{40}}\\ \\ \longrightarrow\sf Total \ Time = \dfrac{3}{2}\ h$

Now calculate the time for 1st 30 km

$\sf \ Speed = \dfrac{Distance }{Time }\\ \\ \longrightarrow\sf 30= \dfrac{30}{T}\\ \\ \longrightarrow\sf T= \cancel{\dfrac{30}{30}}\\ \\ \longrightarrow\sf Time_1 = 1\ hour------(i)$

Now time for next 30 km

$\sf \ Time = \dfrac{Distance }{Speed}\\ \\ \longrightarrow\sf Time_2= \dfrac{30}{s}-----(ii)$

Now calculate the Time

$\sf \ Total \ time = Time _1+ Time_2\\ \\ \longrightarrow\sf \dfrac{3}{2}= 1+\dfrac{30}{s}\\ \\ \longrightarrow\sf \dfrac{3}{2}-1= \dfrac{30}{s}\\ \\ \longrightarrow\sf \dfrac{3-2}{2}= \dfrac{30}{s}\\ \\ \longrightarrow\sf \dfrac{1}{2}\times s= 30\\ \\ \longrightarrow\sf s= 30\times 2\\ \\ \longrightarrow\sf Speed_2= 60km/h$

$\sf{\underline{\ Speed \ of \ bus \ for \ next \ 30 \ km= 60km/h}}$

Answer 2

Refer the attachment above ..

Hope it Helps !!