Question

A Plane left $30$ minutes later than the scheduled time and in order to reach its destination,$1500$ km away it has to increases its speed by $250$ km/hr from its usual speed .Find its usual speed.

Answer 1

Let $x$ be the usual speed of the plane

Increased speed=$x+250$

Time taken by plane in usual circumstaces,$t_1=\frac{distance}{speed}$

$t_1=\frac{1500}{x}$

Time taken by plane due to delay, $t_2=\frac{distance}{x+250}$

Difference in times = Delay in departure

$\frac{1500}{x}-\frac{1500}{x+250}=\frac{30}{60}$

$\frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}$

$\Rightarrow \frac{x+250-x}{x^2+250x}=\frac{1}{3000}$

$x^2+250x-750000=0$

Solving:

$x^2+1000x-750x-750000=0$

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

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

$x=750$

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