Question

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

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

Answer 1

The correct option is C 750 km/hr

Let the usual 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 = 1500 km [Given]
According to the question,
(Scheduled time) - (time taken at increased speed) = 30 minutes = 0.5 hours.

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

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