Q43 of 186 Page 4

A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.

Let the speed of a train = x km/hr

And the speed of a car = y km/hr


Total distance travelled = 600km


According to the question,


If he covers 400km by train and rest by car i.e. (600 – 400) = 200km


Time take = 6hrs 30min


If he travels 200km by train and rest by car i.e. (600 – 200) = 400km


He takes half hour longer i.e. 7 hours


So, total time = train time + car time


We know that,



…(i)


…(ii)



400u + 200v = 6.5 …(iii)


and 200u + 400v = 7 …(iv)


On multiplying Eq. (iii) by 2 and Eq. (iv) by 4, we get


800u + 400v = 13 …(a)


800u + 1600v = 28 …(b)


On subtracting Eq. (a) from Eq. (b), we get


800u + 1600v – 800u – 400v = 28 – 13


⇒ 1200v = 15




On putting the value of v in Eq. (iv), we get



⇒ 200u + 5 = 7


⇒ 200u = 2



So, we get and


⇒ x = 100 and y = 80


Hence, the speed of the train is 100km/hr and the speed of the car is 80km/hr.


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