Question

A plane left 30 mins later than the scheduled time and in order to reach is destination 1500 I'm away in time it has to increase is speed by 250 km/hr from is usual speed . Find it's usual speed.

Answer 1

GIVEN :

• A plane left 30 mins later than the scheduled time.
• It increase speed by 250 km/hr.

TO FIND :

• Usual speed = ?

SOLUTION :

To find the usual speed = ?

We know that,

Let x be the usual speed of the plane.

Increased speed is = x + 250.

The time taken by plane in usual circumstances,

$\sf t_1 \ = \ \dfrac {distance}{speed}$

$\implies \sf t_1 \ = \ \dfrac {1500}{x}$

Time taken by plane due to delay,

$\implies \sf \dfrac {distance}{x + 250}$

Difference in times = Delay in departure.

$\implies \sf \dfrac {1500}{x} \ - \ \dfrac {1500}{x+250}$

$\implies \sf \dfrac {x + 250 - x}{x^{2} + 250x}$

$\implies \sf x^{2} \ + \ 250x \ - \ 750000 \ = \ 0$

$\implies \sf x^{2} \ + \ 1000x \ - \ 750x \ - \ 75000 \ = \ 0$

$\implies \sf x(x + 1000) \ - \ 750(x + 1000) \ = \ 0$

$\implies \sf (x - 750) (x + 1000) \ = \ 0$

$\qquad \qquad \large \blue {\boxed {\tt x \ = \ 750}}$

$\therefore$ The usual speed of the plane is 750 km/hr.