In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of the flight increased by 30 minutes. The duration of the flight is

Given:

Total Distance = 600 km.

average speed was reduced = 200 km/hr 

the time of flight increased = 30 minutes

Formula Used:

∵ Average Speed = Total Distance / Time

Calculations:

Let, the original duration of flight be t hrs.

So, original average speed = 600/t

Due to bad weather speed of trip is reduced by 200 km/hr and time of flight is increased by 30 minutes i.e. 0.5 hr.

∴ Reduced average speed = (600/t) – 200

And New duration of flight = (t + 0.5) hrs

So, the new average speed = 600/(t + 0.5)

Equating,

\(\begin{array}{l} \Rightarrow \frac{{600}}{t}-200 = \frac{{600}}{{t + 0.5}}\\ \Rightarrow \frac{3}{t}-1 = \frac{3}{{t + 0.5}}\\ \Rightarrow \frac{{3-t}}{t} = \frac{3}{{t + 0.5}} \end{array}\)

⇒ t2 + 0.5t – 1.5 = 0

⇒ 2t2 + t – 3 = 0

⇒ 2t2 – 2t + 3t – 3 = 0

⇒ (t – 1)(2t + 3) = 0

⇒ (t – 1) = 0

∴ t = 1 hr

∴ The duration of the flight is 1 hr.