I Want Right Answer.
A plane left 30 minute 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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Answered by
20
Given,
The Plane left 30 minutes late than it's scheduled time
Distance to the destination is 1500 km
Plane's Speed was increased by 100 kmph from usual speed
Usual Speed = ?
Assume a Variable for Usual speed of the Plane
Let be the usual Speed of the Plane
Note the Increased Speed of the Plane
Increased Speed of the Plane = (x+100) kmph
Note the Distance covered by the Plane
Distance covered the plane = Distance from source to Destination
Distance covered the plane = 1500 kmph
Note the time taken to reach the destination with usual speed and Increased speed.
We have,
Note the relation between the time taken by plane to reach the Destination with both usual speed and Increased speed
Let the time taken to reach the destination with usual speed and with increased speed be and respectively.
Given, the Plane is 30 min Late than it's scheduled time.
If speed is more, time taken will be less.
If Speed is less , time taken will be more.
Time taken to reach the destination with usual speed will be more than the time taken to reach the destination with increased speed.
Expressing in Hours
has to be expressed in Hours as the the Speed is in kmph.
We have,
Substitute and to obtain an equation in one variable.
Cross Multiply
Factorise the Equation to get value of the variable
While equating (x+600) to zero,
a negative value is obtained.
Answered by
5
Let, the usual time taken by the aeroplane = x km/hr
- Distance to the destination = 1500 km
Case (i) :
Speed = Distance / Time = (1500 / x) Hrs
Case (ii) :
Time taken by the aeroplane = (x - 1/2) Hrs
Distance to the destination = 1500 km
Speed = Distance / Time
= 1500 / (x - 1/2) Hrs
Increased speed = 250 km/hr
⇒ [1500 / (x - 1/2)] - [1500 / x] = 250
⇒ 1/(2x2 - x) = 1/6
⇒ 2x2 - x = 6
⇒ (x - 2)(2x + 3) = 0
⇒ x = 2 or -3/2
Since, the time can not be negative, The usual time taken by the aeroplane = 2 hrs and the usual speed = (1500 / 2) = 750 km/hr
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