Question

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

• A. $3\frac{1}{2}$ hours
• B. $5\frac{1}{2}$ hours
• C. $4\frac{1}{2}$ hours
• D. $2\frac{1}{2}$ hours

Answer 1

Answer: (A)

$3\frac{1}{2}$ hours

Let the original speed $=xkm/hr$

$\therefore$ Normal time of flight = $\frac{2800}{x}$ hours ,New speed $=(x-100)km/hr$

$\therefore$ Time of flight, when speed is reduced $=\frac{2800}{x-100}$ hours

According to the given condition, $\frac{2800}{(x-100)}-\frac{2800}{x}=\frac{30}{60}$

$\frac{1}{2}=\frac{2800x-2800(x-100)}{x(x-100)}$

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

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

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

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

$\Rightarrow x-800=0$

$x+700=0$

$\Rightarrow x=800,-700$

Neglecting the -ve value.

Original speed of the are craft = $800km/hr$

Original duration of flight $=\frac{2800}{800}=3\frac{1}{2}hours$