Question

out of a distance of 360km if 240km is covered by bus and rest by Train, it takes 8hrs to complete the journey. However if 120km is travelled by the bus and the rest by train, it takes one hour less. What is the speed of the bus and the train.

Answer 1

Answer :

We know : Time = $\frac{Dis\tan ce}{Speed}$

Let speed of bus = x
And
Speed of train = y

So, from first condition we get

$$\begin{gathered} \frac{240}{x}+\frac{120}{y}=8 \\ \Rightarrow \frac{240y+\hspace{0.17em}120x}{xy}=8 \\ \Rightarrow 240y+\hspace{0.17em}120x=8xy \\ \mathbf{\Rightarrow }\mathbf{30}\mathbf{}\mathit{y}\mathbf{}\mathbf{+}\mathbf{\hspace{0.17em}}\mathbf{15}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathit{x}\mathit{y}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{}\mathbf{(}\mathbf{\hspace{0.17em}}\mathbf{1}\mathbf{\hspace{0.17em}}\mathbf{)} \end{gathered}$$

And

From second condition we get

$$\begin{gathered} \frac{120}{x}+\frac{240}{y}=7 \\ \Rightarrow \frac{120y+\hspace{0.17em}240x}{xy}=7 \\ \mathbf{\Rightarrow }\mathbf{120}\mathbf{}\mathit{y}\mathbf{}\mathbf{+}\mathbf{\hspace{0.17em}}\mathbf{240}\mathbf{}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{7}\mathbf{}\mathit{x}\mathit{y}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{}\mathbf{(}\mathbf{\hspace{0.17em}}\mathbf{2}\mathbf{\hspace{0.17em}}\mathbf{)} \end{gathered}$$

Now we multiply by 4 in equation 1 and get

120 y + 60 x = 4 xy ------ ( 3 )

Now we subtract equation 3 from equation 2 and get

180 x = 3 xy

3 y = 180

y = 60 , Substitute that value in equation 1 and get

30 ( 60 ) + 15 x = 60x

1800 + 15 x = 60 x

45 x = 1800

x = 40

So,

Speed of bus = 40 km / hr
And
Speed of train = 60 km / hr ( Ans )