a man travels 400 km partly by train and partly by car. if he covers half the distance by train and the rest by car, it takes him 4hrs 30mins. but if he travels 100 km by train and the rest by car it takes him 15 minutes longer . find the speed of train and car.

let speed of train = x
​thus, speed of car = y

 
thus, 200/x + 200/y = 4.5 { 4 hrs. and 30 minutes} 
        let a = 1/x  , b = 1/y
    200a + 200b = 4.5    (1)
 
     Similarly
100a + 300b = 4.75     (2)


​            multiplying 2 throughout (2)
200a + 600b = 9.5 (2)


                By elimination method
            - 400b = -5
            b = 5 /400
           b = 1/80
   thus, y = 80
​     speed of car = 80 km/h

substituting b in (1)
​   200a + 200b =4.5
​    200a + 200/80 = 4.5
  200a + 2.5 = 4.5
   200a = 2
thus  a = 1/100
​ thus  x = 100 km/h
   thus, speed of the train is 100 km/h


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