A train reach a station at a certain time and at a fixed speed. If the train had been 10 km/hr faster, it would have taken 2 hours less than the scheduled time. And, If the train were slower by 12 km/hr, the would have taken 3 hours more than the scheduled time. The length of journey is:
Answers
Answer:
600 km
Step-by-step explanation:
Let:
The speed of the train be x km/hr, the time required for the journey be t hrs, and the distance be d km.
So, we have, in the first case, d = x * t …….(1)
In the second case, if the train is 10 km/hr faster, the speed would be (x+10) km/hr, and the time required would be (t-2) hrs. Thus we have, as the distance would be the same: d = (x+10)*(t-2)
Expanding, we have d = xt - 2x + 10t - 20. Substituting from equation (1), we get the simplified equation: 10t - 2x = 20 …….(2)
In the third case, if the train is 10 km/hr slower, the speed would be (x-10) km/hr, and the time required would be (t+3) hrs. Thus we have, as the distance would be the same: d = (x-10)*(t+3)
Expanding, we have d = xt + 3x - 10t - 30. Substituting from equation (1), we get the simplified equation: 10t - 3x = -30 …….(3)
Solving equations (2) and (3) simultaneously, we get x = 50 km/hr and t = 12 hrs.
Thus, distance d = x * t, that is d = 50 * 12 = 600km