A plane left 30minutes late than its schedued time and in order to reach of destination 1500km away in time .it had to increase its speed by 100 km/hr from the usual speed.find its usual speed.
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hey, there's time difference is 30 minutes and the distance is same and new speed is 100 more than the earlier, it Will an quadratic equation if you still want to know solution
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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
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