Question

An aeroplane takes $1$ hour less for a journey of $1200$ km if its speed is increased by $100$ km/hr from its usual speed. Its usual speed is ___ km/hr.

Answer 1

$\Rightarrow$ Let the usual speed be $xkm/hr$

According to the question,

$\Rightarrow$ $\frac{1200}{x}-\frac{1200}{100+x}=1$

$\Rightarrow$ $\frac{1200(100+x)-1200x}{x(100+x)}=1$

$\Rightarrow$ $120000+1200x-1200x=100x+x^2$

$\Rightarrow$ $120000=100x+x^2$

$\Rightarrow$ $x^2+100x-120000=0$

$\Rightarrow$ $x^2+400x-300x-120000=0$

$\Rightarrow$ $x(x+400)-300(x+400)=0$

$\Rightarrow$ $(x+400)(x-300)=0$

$\Rightarrow$ $x=-400$ and $x=300$

Speed can not be negative.

$\therefore$ Original speed $=300km/hr$

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