Question

An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

Answer 1

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Answer 2

Answer:

The usual speed of the aeroplane is 300 km/hour

Step-by-step explanation:

Let the usual speed of the aeroplane be x km/hour

Distance = 1200 km

$Distance = \frac{Speed}{Time}\\\\\text{Time taken with usual speed = }\frac{1200}{x}\\\\\text{Time taken when speed increase by 100 km per hour = }\frac{1200}{x+100}\\\\\text{Now, according to question, }\\\\\frac{1200}{x}-1=\frac{1200}{x+100}\\\\\implies \frac{1200}{x} -\frac{1200}{x+100}=1\\\\\implies \frac{1200(100+x)-1200x}{x(100+x)}=1\\\\\implies x^2+100x-120000=0\\\implies (x-300)\cdot (x+400)=0\\\text{Since, the speed cannot be negative}\\\bf\implies x=Speed = 300\textbf{ km per hour}$

Hence, the usual speed of the aeroplane is 300 km/hour