Question

An aeroplane left $30$ minutes later then its scheduled time and in order to reach its destination $1500$ km away in time it has to increase its speed by $250$ km/h from its usual speed. Determine its usual speed

• A. $700$ km/h
• B. $750$ km/h
• C. $770$ km/h
• D. $800$ km/h

Answer 1

The correct option is B $750$ km/h

Let $x$ = usual speed

Usual time taken to reach destination:

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

Time to reach destination is now t - 0.5 (half hour), and speed is now x + 250

$t-0.5=\frac{1500}{x+250}$

$\Rightarrow 1500x=(1500-0.5x)(x+250)$

$\Rightarrow 1500x=-0.5x^2+125x+375000$

$\Rightarrow 0.5x^2+125x=375000$

$\Rightarrow x^2+250x=750000$

$\Rightarrow x^2+250x+15625=750000+15625$

$\Rightarrow (x+125{)}^2=765625\Rightarrow x+125=875\Rightarrow x=750$

Usual speed $=750$ km/hr