Question

In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.

Hint:

Always convert all time units (minutes to hours) to match the speed units (km/h) before setting up the equation.

Answer 1

Step 1: Understanding the Concept:
Time taken is inversely proportional to speed for a fixed distance. We use the formula: Time = Distance / Speed.
Step 2: Key Formula or Approach:
Let usual speed $= x$ km/h. Distance $= 600$ km.
Usual time $t_1 = 600/x$. Reduced speed time $t_2 = 600/(x-200)$.
Condition: $t_2 - t_1 = 30 \text{ min} = 0.5 \text{ hours}$.
Step 3: Detailed Explanation:
\[ \frac{600}{x - 200} - \frac{600}{x} = \frac{1}{2} \]
Multiply by $2x(x-200)$:
\[ 1200x - 1200(x - 200) = x(x - 200) \]
\[ 1200x - 1200x + 240000 = x^2 - 200x \]
\[ x^2 - 200x - 240000 = 0 \]
Factoring the quadratic equation:
\[ x^2 - 600x + 400x - 240000 = 0 \]
\[ (x - 600)(x + 400) = 0 \implies x = 600 \text{ km/h} \text{ (as speed }>0) \].
Scheduled duration $= 600 / 600 = 1$ hour.
Step 4: Final Answer:
The scheduled duration of the flight is 1 hour.