Question

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

Answer 1

Step 1: Given

Total distance, $d=600km$

Average speed was reduced by $200km/hr$

Time of the flight increased by $30$minutes

Step 2: Find the new average speed of the flight

Let $t$ be the original duration of the flight

The original average speed of the flight was $\frac{600}{t}$

Hence, the new average speed is

$s=$Original speed - Reduced speed$=\frac{600}{t}-200$

Step 3: Find the new duration of the flight

Let the new duration be $t_1$

$t_1=$Original duration + Increased time$=t+0.5hr$

Step 4: Find the new average speed

The new average speed$$\begin{gathered} =\frac{d}{t_1} \\ =\frac{600}{t+0.5} \end{gathered}$$

Step 5: Equate the new average speeds

$$\begin{gathered} \frac{600}{t}-200=\frac{600}{t+0.5} \\ Dividingby200onboththesides,weget \\ \Rightarrow \frac{3}{t}-1=\frac{3}{t+0.5} \\ \Rightarrow t^2+0.5t-1.5=0 \\ \Rightarrow (t-1)(2t+3)=0 \\ \Rightarrow t=1 \end{gathered}$$

Therefore, the duration of the flight is $1$ hour.