A man travels 370 km partly by train and pa by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But, If he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.
Answers
Answer:
Speed of train is 100km/hr and speed of car is 80 km/hr.
Step-by-step explanation:
Given:-
The total distance of 370 km is partly covered by train and partly by car.
Let:-
The speed of the train be x km/hr and the speed of the car be y km/hr.
In first case,
The distance covered by train = 250km
The distance covered by car will be [total distance - distance covered by train]
=> [370-250]km
=> 120km
We have:-
Total time taken by this journey = 4hrs
As we know that
=> speed = distance /time
Therefore:-
Time = distance /speed
By considering the same formula the equation can be represented as,
250/x + 120/y = 4............(i)
And in the second case,
The distance covered by train = 130km
The distance covered by car = [370 -130]
=> 240km
Total time taken in this journey
= (4 +18/60)hrs
[As time = distance /speed]
We get the required equation as,
130/x + 240/y = 4 +18/60........(ii)
130/x + 240/y = 4.3.....(ii)
Now on solving equation (i) & (ii),
=> 250/x + 120/y = 4
=> 130/x + 240/y = 4.3
By substitution method of linear equation in two variables :
Let:-
1/x = u and 1/y = v
Then:-
=> 250u + 120v = 4
=> 130u + 240v = 4.3
Now on solving further,
=> 25u + 12v = 0.4.... (iii)
=> 13u + 24v = 0.43.... (iv)
Multiply equation (iii) by 2,
=> 50u + 24v = 0.8.... (v)
=> 13u + 24v = 0.43.... (vi)
Subtracting equation (vi) from (v)
we get,
=> (50u + 24v) - (13u + 24v) = 0.8 - 0.43
=> 50u + 24v - 13u - 24v = 0.37
=> 37u = 0.37
=> u = 0.37/37
=> u = 1/100
Now on Putting the value of u in equation (iii),
=> 25/100 + 12v = 0.4
=> 1/4 + 12v = 2/5
=> 12v = (2/5 - 1/4)
=> v = 3/20*1/12
=> v = 1/80
As x = 1/u......{as u = 1/100}
=> x = 100
And as y = 1/v......{as v = 1/80}
=> y = 80
Therefore-:
Speed of train is 100km/hr and speed of car is 80 km/hr.