Question

Mala travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 80 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.​

Answer 1

Question :

Mala travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 80 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Answer :

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

$\bold { \underline{{According \: to \: question : }}}$

$\begin{gathered} \tt\frac{60}{u} + \frac{120}{v} = 4 \: \: ...(1) \\ \\ \\ \tt \: \frac{100}{u} + \frac{200}{v} = 4 + \frac{10}{60} = \frac{20}{6} \: \: ...(2) \end{gathered}$

Let ,

$\begin{gathered} \tt{ \frac{1}{u} = p \: \: and \: \: \frac{1}{v} = q} \end{gathered}$

The given equations reduce to :

$\begin{gathered} \: \tt \: 60 p + 240q = 4 \: \: ...(3) \\ \\ \tt \: 100p + 200q = \frac{25}{6} \\ \\ \tt \: 600p + 1200q = 25 \: \: ...(4) \end{gathered}$

Multiplying equation (3) by 10, we get,

$\bold{600p + 2400q = 40 \: \: ...(5)}$

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

$\begin{gathered} \tt \bold1200q = 15 \\ \\ \tt q = \frac{15}{1200} = \frac{1}{80} \end{gathered}$

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

$\tt \implies{60p + 3 = 4}$

$\tt \implies{60p = 1}$

$\tt \implies{p = \large \frac{1}{60} }$

$\begin{gathered} \: \sf \: p = \tt{\frac{1}{u}} = \tt {\frac{1}{60}} \: \: , \: q = \tt\frac{1}{v} = \frac{1}{80} \end{gathered}$

u = 60 kmph and v = 80 kmph

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