Question

A plan left 30 min late then its scheduled time and in order to reach the destination 1500 km away in time it had to increase its useual speed. find its useual speed

Answer 1

speed=distance/time
speed=1500/30
speed=50

Answer 2

$\sf\red{\underline{Question:}}$

A plan left 30 min late then its scheduled time and in order to reach the destination 1500 km away in time it had to increase its useual speed. find its usual speed.

$\sf\red{\underline{Solution:}}$

Let usual speed of aeroplane = X km

Total distance to reach the destination = 1500 km

A.T.Q

$\sf\green{Case \:1}$

$Time =\frac{Distance}{speed} \\ \\ \implies \frac {1500}{x}h$

$\sf\green{Case \:2}$

Let (x+100)km/hr be new speed of aeroplane

$New \: Time =\frac{Distance}{speed} \\ \\ \implies \frac {1500}{x+100}h$

$\sf\blue{Original~time-new~time}$

$\implies 30min \frac{1500}{x} -\frac{1500}{x+100}\\ \\ \implies \frac{30}{60}\\ \\ \implies \frac{1500}{x} - \frac{1500}{x+100} =\frac{1}{2}h\\ \\ \implies 1500[\frac{1}{x}-\frac{1}{x+100}]= 1/2 \\ \\ \implies 1500 \times 2 \frac{x+100-x}{x(x+100)}=1\\ \\ \implies 3000\frac{100}{x^2+100x}=1\\ \\ \implies 3,00,000=x^2 +100x$

$x^2+100x-3,00,000=0 \\ \\ \implies x^2 +600x-500x-300000=0 \\ \\ \implies x(x+600)-500(x+600)=0 \\ \\ \implies (x+600)(x-500)=0 \\ \\ \implies x=-600,500$

Since, the speed cannot be negative.

$\sf\red{Hence~speed~of ~aeroplane =500~km}$