a train takes 2 hours less for a journey of 300km if its speed is increased by 5km/hr from its usual speed .find the usual speed of the train.
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Define x:
Let the usual speed be x
Original Speed:
Distance = 300 km
Time = Distance ÷ Speed
Time = 300/x
After the increased in speed:
Distance = 300 km
Time = Distance ÷ Speed
Time = 300/(x + 5)
Solve x:
Given that the time difference is 2 hours
300/x - 300/(x + 5) = 2
300(x + 5) - 300x = 2(x)(x + 5)
300x + 1500 - 300x = 2x² + 10x
2x² + 10x - 1500 = 0
x² + 5x - 750 = 0
(x - 25)(x + 30) = 0
x = 25 or x = - 30 (negative, rejected)
Find the usual speed:
Speed = x = 25 km/h
Answer: The usual speed is 25 km/h
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