Question

A plane left $30$ minutes late than its scheduled time and in order to reach the destination $1500km$ away in time, it had to increase its speed by $100km/h$ from the usual speed. Find its usual speed.

Answer 1

Let the usual speed be $xkm/hr$.

Then, the speed taken $=(x+100)km/hr$

Distance $=1500km$

Usual time $=\frac{distance}{usualspeed}=\frac{1500}{x}hrs$

Time taken $=\frac{1500}{x+100}hrs$

It is given that $Timetaken=Usualtime-0.5hrs$

$\Rightarrow \frac{1500}{x}-\frac{1500}{x+100}=\frac{1}{2}$

$\Rightarrow \frac{1500(x+100)-1500x}{x(x+100)}=\frac{1}{2}$

$\Rightarrow x^2+100x=1500\times 100\times 2$

$\Rightarrow x^2+100x-300000=0$

$\Rightarrow x=\frac{-100\pm \sqrt{{100}^2+4\times 300000}}{2}=\frac{-100\pm 1100}{2}=500or-600$

Since speed cannot be negative, $x=500km/hr$

$\therefore$ The usual speed of the plane is $500km/hr$.