A person covers a distance of 900 km partly by train and partly by car. If he travels
200 km by train rest by car it takes 12 hours and if he covers 300 by train and rest by car
it takes him 13 hours 30 minutes to cover that distance. Find the speed of train and car.
Answer:
Speed of train = 40 km/hr and speed of car = 100 km/hr
Step-by-step explanation:
Let the speed of train be x and speed of car be y
According to the first condition ,
200/x + 700/y = 12 ( Since , Time = Distance / speed ) ________ (1)
According to second condition ,
300/x + 600/y = 13 + 30/60
Therefore ,
300/x + 600/y = 13 + 1/2 = 27/2 ( Since 1 hr = 60 mins ) _______ (2)
Now,
Take 1/x = m and 1/y = n
Therefore,
200 m + 700 n = 12 _______ (3)
300 m + 600 n = 27/2 _______ (4)
Now,
Multiplying equation 3 by 3 and equation 4 by 2 , we get ,
600 m + 2100 n = 36 _____ (5)
600 m + 1200 n = 27 _______ (6)
Subtracting equation 6 from equation 5 , we get ,
600 m + 2100 n – ( 600 m + 1200 ) = 36 – 27
600 m + 2100 n – 600 m – 1200 n = 9
900 n = 9
n = 9/900
n= 1/100 .
substituting n = 1/100 in equation 3 , we get ,
200 m + 700 ( 1/100 ) = 12
200 m + 7 = 12
200 m = 5
m = 5/200
m = 1/40
Resubstituting 1/x = m and 1/y = n , we get ,
x = 40 and y = 100