Question

Ramesh travels 760km to his home partly by train and partly by car . He takes 8 hours if he travels 160km by train and the rest by car .he takes 12 minutes more if he travels 240km by train and the rest by car . Find the speed of the train and car respectively.

Answer 1

Let the speed of train = x km/hr and speed of car= y km/hr

Case 1
Distance travelled by train = 160 Km
Distance travelled by car = 760-160 = 600 km
Time taken by train = 160/x hr
Time taken by car = 600/y hr
Total time taken = 160/x+600/y hr160/x+600/y = 8 hr --------------- Equation 1


Case 2
Distance travelled by train = 240 Km
Distance travelled by car = 760-240 = 520 km
Time taken by train = 240/x hr
Time taken by car = 520/y hr
Total time taken = 240/x + 520/y hr
240/x+520/y = 8+12/60 (12 minutes=12/60 hr)
240/x+520/y = 41/5 --------------- Equation 2

Multiply equation 1 by 3 and equation 2 by 2 and subtract equation 2 from equation 1
1800/y - 1040/y = 24-82/5
760/y = 38/5
y = (760 x 5)/38
= 100 km/hr
Putting y = 100 in equation 1
160/x + 600/100 = 8
x = 80 km/hr

Speed of Car = 100 km/hr
Speed of train = 80 km/hr