Question

A plane left 30 minutes later than its scheduled time. In order to reach the destination which is 1500 km away on time, it has to increase its speed by 250 km/hr. Find its original speed.

• A. 1000 km/hr
• B. 750 km/hr
• C. 800 km/hr
• D. 680 km/hr

Answer 1

The correct option is B 750 km/hr

Let the original speed of plane be $x$ km/hr

and the increased speed of the plane be $y$ km/hr.
$\Rightarrow y=(x+250)$ km/hr
Distance $=1500km$ [Given]
According to the question,
(Scheduled time) - (New time ) = 30 minutes

$\frac{1500}{x}-\frac{1500}{y}=\frac{1}{2}\frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}[\because Time=\frac{Distance}{Speed}]\Rightarrow \frac{1500x+375000-1500x}{x(x+250)}=\frac{1}{2}$

$\Rightarrow$ $x(x+250)=750000$
$\Rightarrow x^2+250x-750000=0$
$\Rightarrow x^2+1000x-750x-750000=0$
$\Rightarrow$ $x(x+1000)-750(x+1000)=0$
$\Rightarrow$ $(x-750)(x+1000)=0$
$\Rightarrow$ $x=750orx=-1000$
Since speed cannot be negative.
$\therefore$ The original speed is $750$ km/hr.