Question

A man covers a certain distance on a toy train. If the train moved 4 km/hr faster, it would take 30 minute less and if it moved 2 km/hr slower, it would have taken 20 minutes more, then the distance (in km) is _________.

Answer 1

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Answer 2

Step-by-step explanation:

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Let distance covered by man is D , original speed is v and original time taken by him is t.

so, D = vt .......(1)

case 1 : new speed of train = (v + 4) km/h , new time taken = (t - 1/2) hr

so, D = (v + 4)(t - 1/2) ........(2)

case 2 : new speed of train = (v - 2) km/h , new time taken = (t + 1/3) hr [as 20min = 1/3 hr ]

so, D = (v - 2)(t + 1/3) ........(3)

from equations (1) and (2),

vt = vt - v/2 + 4t - 2

⇒4t - v/2 = 2 .........(4)

from equations (1) and (3),

vt = vt + v/3 - 2t - 2/3

⇒v/3 - 2t = 2/3 ........(5)

from equations (4) and (5),

2v/3 - v/2 = 2 + 4/3 = 10/3

⇒v/6 = 10/3

⇒v = 20 km/hr and t = 3 hrs

so, D = vt = 20 × 3 = 60 km