A passenger train takes 2 hours less for a journey of 300 km,  if itsspeed is increased by 5 km/h from its usual speed. Find its usualspeed.
Let the usual speed be x km/hr.
Distance travelled by a passenger train = 300 km.
We know that
Time = Distance / Speed
Time taken by a passenger train to travel with the speed of
Time taken by a passenger train to travel with the speed of
By the given condition
1500 = 2(x 2 + 5x)
1500 = 2x 2 + 10x
On rearranging
2x 2 + 10x – 1500 = 0
x 2 + 5x – 750 = 0
x 2 + 30x – 25x – 750 = 0
x(x + 30) – 25(x + 30) = 0
(x - 25)(x + 30) = 0
x - 25 = 0 or x + 30 = 0
x = 25 or x = – 30
Since x is the usual speed it cannot be negative.
Therefore, we reject the solution x = –30.
Thus the usual speed is 25 km/hr.
Checking:
Time taken by a passenger train to travel with the speed of
Time taken by a passenger train to travel with the speed of
Thus, a passenger train takes 2 hours less for a journey if its speed is increased by 5 km/hr from its usual speed.
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