#### Question

A passenger, while boarding the plane, slipped form the stairs and got hurt. The pilot took the passenger in the emergency clinic at the airport for treatment. Due to this, the plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/hour than the usual speed. Find the usual speed of the plane

What value is depicted in this question?

#### Solution

Let the usual speed of the plane be *x* km/h.

Let the time taken by the plane to reach the destination be *t*_{1}

`:.t_1=1500/x`

To reach the destination on time, the speed of the plane was increased to (*x* + 250)km/h.

`:.t_2=1500/(x+250)`

Given: *t*_{1} − *t*_{2} = 30 min

Now,

`1500/x-1500/(x+250)=30/60`

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

⇒750000=x^{2}+250x

⇒x^{2}+250x−750000=0

On solving the equation, we get

x=750

Thus,

Usual speed of the plane = 750 km/h

The value depicted in this question is that of humanity. The pilot has set an example of a good and responsible citizen of the society