Question

A man travels 400km partly by train and partly by car. If he covers half the distance by train and rest by
car, it takes him 4hours 30minutes. But if he travels 100km by train and rest by car, he takes 15minutes
longer. Find the speed of the train and that of the car.

Answer 1

\huge\green{}

$\huge\green{speed = \frac{distance}{time} }$

$time = \frac{distance}{speed}$

let the speed of car be X

let the speed of car be Xlet the speed of train be Y

$\huge\pink{case \: 1}$

$distance \: covered \: by \: train \: = 200km$

$distance \: covered \: by \: car \: = 200km$

$time \: taken = 4 \times 60 + 30min \\ = 240 + 30 \: min \\ = 270 \: min$

$\frac{200}{x} + \frac{200}{y} = 270 \: min$

$\huge\pink{case \: 2}$

$distance \: covered \: by \: train \: =100 km$

$distance \: covered \: by \: car \: =300km$

$time \: taken = 4 \times 60 + 30min + 15\\ = 240 + 30 \: + 15min \\ = 285 \: min$

$\frac{100}{y} + \frac{300}{x} = 285 \: min$

$let \: \frac{1}{x} \: be \: u \: and \: \frac{1}{y} \: be \: v \:$

$100v + 300u = 285$

$200x + 200y = 270$

$v + 3u = 2.85$

$v + u = 1.35$

__ __ ___

$2u = 1.5$

$u = \frac{15}{20} \\ = \frac{3}{4} = \frac{1}{x} \\ x = \frac{4}{3} \\ x = 1.3 \: km \: per \: hr$

$v = 0.15 \\ = \frac{15}{10} \\ = \frac{3}{2} = \frac{1}{y} \\ y = \frac{2}{3} \\ y = 0.67 \: km \: per \: hour$

using elimination method

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