A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time,it had to increase its speed by 100 km/h from the usual speed.Find its usual speed
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Solution :-
Let the original speed of train be x km/hr
New speed = (x + 100) km/hr
We know that,
Time = Distance / Speed
Given : A plane left 30 minutes or 1/2 hours later than the scheduled time.
According to the question,
=> 1500/x - 1500/(x + 100) = 1/2
=> (1500x + 15000 - 1500x)/x(x + 100) = 1/2
=> 2(15000) = x(x + 100)
=> 30000 = x² + 100x
=> x² + 100x - 30000 = 0
=> x² + 600x - 500x - 30000 = 0
=> x(x + 600) - 500(x + 600) = 0
=> (x - 500) (x + 600) = 0
=> x = 500 or x = - 600
∴ x ≠ - 600 (Because speed can't be negative)
Hence,
Its usual speed = 500 km/hr
Let the original speed of train be x km/hr
New speed = (x + 100) km/hr
We know that,
Time = Distance / Speed
Given : A plane left 30 minutes or 1/2 hours later than the scheduled time.
According to the question,
=> 1500/x - 1500/(x + 100) = 1/2
=> (1500x + 15000 - 1500x)/x(x + 100) = 1/2
=> 2(15000) = x(x + 100)
=> 30000 = x² + 100x
=> x² + 100x - 30000 = 0
=> x² + 600x - 500x - 30000 = 0
=> x(x + 600) - 500(x + 600) = 0
=> (x - 500) (x + 600) = 0
=> x = 500 or x = - 600
∴ x ≠ - 600 (Because speed can't be negative)
Hence,
Its usual speed = 500 km/hr
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