Question

a plane left 30 min later than the scheduled time and in order to reach in ventilation 1500 km away in time it has to increase its speed bike 250 km per hour from it is a speed find out user speed

Answer 1

Answer:

Step-by-step explanation:

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.

Hope this helps you.

Answer 2

Solution :-

Let the original speed of train be x km/hr

New speed = (x + 250) 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 + 250) = 1/2

=> (1500x + 37500 - 1500x)/x(x + 250) = 1/2

=> 2(37500) = x(x + 250)

=> 75000 = x² + 250x

=> x² + 250x - 75000 = 0

=> x² + 1000x - 750x - 75000 = 0

=> x(x + 1000) - 750(x + 1000) = 0

=> (x - 750) (x + 1000) = 0

=> x = 750 or x = - 1000

∴ x ≠ - 1000 (Because speed can't be negative)

Hence,

Its usual speed = 750 km/hr