Question

Mala travels $300km$ to her home partly by train and partly by bus. She takes $4$ hours if she travels $60km$ by train and the remaining by bus. If she travels $100km$ by train and the remaining by bus, she takes $10$ minutes longer. Find the speed of the train and the bus separately.

Answer 1

Let the speed of train and bus be u kmph and v kmph repectively.

According to the question

$\frac{60}{u}+\frac{240}{v}=\mathrm{4........}\left(1\right)$

$\frac{100}{u}+\frac{200}{v}=4+\frac{10}{60}=\frac{25}{6}.....\left(2\right)$

Let

$\frac{1}{u}=p$ and $\frac{1}{v}=q$

The given equations reduce to:

$60p+240q=\mathrm{4.....}\left(3\right)$

$100p+200q=\frac{25}{6}$

$600p+1200q=\mathrm{25.....}\left(4\right)$

Multiplying equation (3) by 10, we get

$600p+2400q+\mathrm{40.....}\left(5\right)$

Subtracting equation (4) from (5), we get

$1200q=15$

$q=\frac{15}{1200}=\frac{1}{80}$

Substituting the value of q in equation (3), we get

$60p+3=4$

$60p=1$

$p=\frac{1}{60}$

$\therefore p=\frac{1}{u}=\frac{1}{60},q=\frac{1}{v}=\frac{1}{80}$

$u=60kmph,v=80kmph$

Thus, the speed of train and the speed of bus are 60 kmph and 80 kmph respectively.