Question

a men travels 370 km 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 longer. Find the speed of the train and car.

Answer 1

Let the speed of train and bus be u km/h and v km/h respectively.

According to the given information,

60/u + 240/v = 4 ... (i)

100/u + 200/v = 25/6 ... (ii)

Putting 1/u = p and 1/v = q in the equations, we get

60p + 240q = 4 ... (iii)

100p + 200q = 25/6

600p + 1200q = 25 ... (iv)

Multiplying equation (iii) by 10, we get

600p + 2400q = 40 .... (v)

Subtracting equation (iv) from (v), we get1200q = 15

q = 15/200 = 1/80 ... (vi)

Putting equation (iii), we get

60p + 3 = 4

60p = 1

p = 1/60

p = 1/u = 1/60 and q = 1/v = 1/80

u = 60 and v = 80

Hence, speed of train = 60 km/h and speed of bus = 80 km/h.