A Plane Left 30 Minutes Later later than the scheduled time and in order to reach the desination, 1500km away in time. It has to increase the speed by 100km/h from the usual seed. Find the usual speed?
Answers
Answer:
- The usual speed = 500 km/h
Given :
- A Plane Left 30 Minutes Later later than the scheduled time and in order to reach the desination, 1500km away in time.
- It has to increase the speed by 100km/h from the usual seed.
To find :
- The usual speed = ?
Step-by-step explanation:
Let usual speed of plane is equal to x kilometre per hour.
Time taken = 1500/x
Now increased speed of plane = x + 100
Time = 1000 /x + 100
According to the question :
1500/x = 1500/x + 100 = 1/2
1500(x + 100) - 1500(x)/x(x+100) = 1/2
1500[x+100-x]/x² + 100x × (1/2)
150000 × 2 = x² + 100x
300000 = x² + 100x
x² + 100x - 300000
x² + 600x - 500x - 300000
x(x + 600) - 500(x + 600)
(x - 500) (x + 600)
Here, value of x = 500 and 600
Therefore, the usual speed = 500 km/h
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