a plane left 30 min late then its scheduled time and in order to reach the destination 1500 km away in time it had to increase its speed by 100km per hour from the usual speed .Find the usual speed
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the ans issssssssss 98km/hrs
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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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