Question 3:
A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Answer:
Let the speed of the train be x km/h and the time taken by train to travel the given distance be t hours and the distance to travel was d km. We know that,
Or, d = xt (i)
Using the information given in the question, we obtain
By using equation (i), we obtain
3x − 10t = 30 (iii)
Adding equations (ii) and (iii), we obtain
x = 50
Using equation (ii), we obtain
(−2) × (50) + 10t = 20
−100 + 10t = 20
10t = 120
t = 12 hours
From equation (i), we obtain
Distance to travel = d = xt
= 50 × 12
= 50 × 12
Hence, the distance covered by the train is 600 km.
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