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 flight increased by 30 minutes. The duration of the flight is: (Speed)

প্রশ্নে বলা আছে, 600 km দূরত্বে একটি ফ্লাইট খারাপ আবহাওয়ার কারণে গড় গতিবেগ 200 km/hr কমিয়ে দেয়া হলো এবং এর কারণে ফ্লাইটটি 30 মিনিট দেরী হলো। 600 km দূরত্ব অতিক্রমে ফ্লাইটটির কত সময় লাগে?

Here, Distance, D = 600km

Let, Time=t & Speed = s

According to the question,

D= st

$$\begin{gathered} \Rightarrow 600 = st \\ \Rightarrow x = \frac{600}{t} . . . . . . . . . . \left(i\right) \end{gathered}$$

From 2^nd condition,

$$\begin{gathered} \left(s -200\right) \left(t + \frac{1}{2}\right) = 600 \\ \Rightarrow \left(\frac{600}{t} - 200\right) \left(t + \frac{1}{2}\right) = 600 \\ \Rightarrow \left(\frac{600- 200t}{t} \right) \left(\frac{2t + 1}{2}\right) = 600 \\ \Rightarrow (600-200t) (2t+ 1) = 1200t \\ \Rightarrow 1200t+600-400t^2- 200t = 1200t \\ \Rightarrow 1000t-400t^2+ 600 = 1200t \\ \Rightarrow 400t^2+1200t - 1000t-600=0 \\ \Rightarrow 400t^2+200t - 600 = 0 \\ \Rightarrow 100(4t^2+2t-6)=0 \\ \Rightarrow 4t^2+2t-6=0 \\ \Rightarrow 4t^2+6t-4t-6=0 [Dividing both sides by 100] \\ \Rightarrow 2t (2t+3)-2 (2t+3)=0 \\ \Rightarrow (2t+3) (2t-2)=0 \\ \Rightarrow t =- \frac{3}{2} and t =1 \end{gathered}$$

As, t cannot be negative

So, t = 1 hour

∴ Duration of the journey = Normal time + Extra/Delay = 1h+0.5h = 1.5 hour 

Answer: 1.5 hour