plane left 30 minutes late than its scheduled time and in order to reach the destination thousand 500 km away in time it had to increase its speed by 100 km per hour from usual speed find its usual speed
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Given:
Late = 30 min
Distance = 1500 km
Speed increase = 100 km / hr
To find:
The usual speed.
Solution:
By formula,
Speed = Distance / Time
Since the time is unknown,
Consider x for time,
Speed original = 1500 / x
Time taken = ( x - 1 / 2 )
Therefore,
Substituting the value of x,
Speed new = 1500 / (x - 1/2)
Speed New - Speed original = 100
( 1500 / ( x - 1 / 2 ) ) - ( 1500 / x ) = 100
150 ( ( 10 / x - 1 / 2 ) - 10 / x = 100
30 x -30 x +15 = 2x^2 - x
15 = 2x^2 - x
2x^2 - x -15 = 0
Solving,
x = -5/2
x = 3
As time cannot be negative,
The usual time taken by the plane is 3 hr
Speed original = ( 1500 / 3 ) = 500 km / hr
Hence, the usual speed of the plane is 500 km / hr.
Hey mate...
Here is your answer
Distance = 1500 km
Speed increase = 100 km / hr
To find:
The usual speed.
Solution:
By formula,
Speed = Distance / Time
Since the time is unknown,
Consider x for time,
Speed original = 1500 / x
Time taken = ( x - 1 / 2 )
Therefore,
Substituting the value of x,
Speed new = 1500 / (x - 1/2)
Speed New - Speed original = 100
( 1500 / ( x - 1 / 2 ) ) - ( 1500 / x ) = 100
150 ( ( 10 / x - 1 / 2 ) - 10 / x = 100
30 x -30 x +15 = 2x^2 - x
15 = 2x^2 - x
2x^2 - x -15 = 0
Solving,
x = -5/2
x = 3
As time cannot be negative,
The usual time taken by the plane is 3 hr
Speed original = ( 1500 / 3 ) = 500 km / hr
Hence, the usual speed of the plane is 500 km / hr.