Question

In a flight of $2800km,$ an aircraft was slowed down due to today's weather. It's average speed for the trip was reduced by $100km/$hour and the time increased by $30$ minutes. Find the original duration of the flight.

Answer 1

Let the speed of aircraft be $xkm/h$

Distance travelled $=2800km$

Time taken $=\frac{\text{Distance}}{\text{Speed}}=\frac{2800}{x}$ hours

Given that when the speed is reduced by $100km/h,$ New speed $=(x–100)km/h$, time is increased by $30$ minutes

That is, $30$ minutes $=\frac{30}{60}$ hour $=\frac{1}{2}$ hour

Time taken after the speed was reduced $=\left[\frac{2800}{(x–100)}\right]$ hour

$\therefore \left[\frac{2800}{x–100}\right]=\frac{2800}{x}+\frac{1}{2}$

$\Rightarrow \left[\frac{2800}{x–100}\right]-\frac{2800}{x}=\frac{1}{2}$

$\Rightarrow 2800\left[\frac{x-(x-100)}{x(x-100)}\right]=\frac{1}{2}$

$\Rightarrow x^2-100x-560000=0$

$\Rightarrow x^2-800x+700x-560000=0$

$\Rightarrow x(x-800)+700(x-800)=0$

$\Rightarrow (x+700)(x-800)=0$

$\Rightarrow x=-700$ or, $800$

Since speed cannot be negative, $x=800.$

Thus original duration of the flight $=\frac{2800}{800}=\frac{7}{2}$ hours $=3$ hours $30$ minutes