Question

a man Travels 370 km partly by train and partly by car. if he covers 250 km by train and the rest by car, it takes in 4 hours . but, if he travels 130 km by train and rest by car ,he takes 18 minutes longer .find the speed of the train and that of the car

Answer 1

Let the speed of the car be C kmph
Let the speed of the train be T kmph

4 hours = 250 km / T kmph + (370 - 250) km / C kmph

          4 = 250/T + 120/C                          ---------------- equation 1

4 hrs 18 minutes = 130 km / T kmph + (370 - 130)km / C kmph

       258/60 = 4.3 = 130 / T + 240 / C      --------------- equation 2

 

Multiply equation 1 by 2 and subtract equation 2 from it.

       8 - 4.3 = 500/T - 130/T + 240/C - 240/C

       3.7 = 370 / T

       T = 370/3.7 = 100 kmph

Substitute the value of T in equation 1 to get,

 

       4 = 250/T + 120/C            ---------- equation 1

       4 = 250/100 + 120/C

       4 - 2.5 = 120/C

       C = 120/1.5 = 80 kmph

 

The train runs at 100 kmph and the car runs at 80 kmph

Answer 2

the answer is for car 80kmph
and for train 100kmph