A man travels 370km partly by train and partly by car . if he covers 250 km by train and the rest by car he takes 4 hours but if he travels 130 km by train and the rest by car he takes 18 minutes more . find the speed of the train and car
Answers
Let the speed of the train be x and the car be y :
If he covers 250 km by train he covers (370 - 250) km by car.
Train = 250km
Car = 370 - 250 = 120
Time by train = 250/x
Time by car is = 120/y
250/x + 120/y = 4....... 1
If he travels 130km by train, he travels (370 - 130)
Distance by train 130km
Distance by car 240km
Time taken is :
4 + 18/60 = 4,3/10 hrs
= 4. 3hrs
Time by train = 130/x
Time by car = 240/y
130/x + 240/y = 4.3.......... 2
From equation 1 we can get x :
250/x + 120/y = 4
250/x = 4 - 120/y
250 = 4x - 120x/y
250 = 4x (1 - 30/y)
x = 250/(4 - 120/y)
Putting this value in 2:
130 × (4 - 120/y) /250 + 240/y = 4.3
(52 - 1560/y) /25 + 240/y = 4.3
52 - 1560y + 6000/y = 107.5
52y - 1560 + 6000 = 107.5y
-55.5y - 1560 +6000 = 0
-55. 5y = -4440
y = 4440/55.5
y = 80
Substituting the value of y in the first equation we have :
250/ x + 120/80 = 4
250/x + 1.5 = 4
250/x = 4 - 1.5
250/x = 2.5
250 = 2.5x
X = 250/2.5
X = 100 km/h
Speed of car = 80 km/h
Speed of the train = 100 km/h