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

Let the original speed of the aircraft be \( S \) km/h and the original time taken for the flight be \( T \) hours.

The total distance is 600 km, so we have the following two equations:

### 1. Original situation (without bad weather):
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
600 = S \times T \quad \text{(Equation 1)}
\]

### 2. After the speed is reduced by 200 km/h:
The new speed becomes \( S - 200 \) km/h, and the time increases by 30 minutes, which is \( \frac{1}{2} \) hours. Therefore, the new time is \( T + \frac{1}{2} \).

The new equation for distance is:
\[
600 = (S - 200) \times \left(T + \frac{1}{2}\right) \quad \text{(Equation 2)}
\]

Now, let's solve these two equations to find \( T \) (the original duration of the flight).

### Step 1: Express \( S \) from Equation 1
From Equation 1:
\[
S = \frac{600}{T}
\]

### Step 2: Substitute \( S \) into Equation 2
Substitute \( S = \frac{600}{T} \) into Equation 2:
\[
600 = \left(\frac{600}{T} - 200\right) \times \left(T + \frac{1}{2}\right)
\]

Now, we will simplify this equation to find \( T \).The solution for the original duration of the flight \( T \) is 1 hour (since the negative time, -1.5 hours, is not physically meaningful in this context).

Thus, the original duration of the flight was 1 hour.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. What would be the original speed of the aircraft?
2. If the time increased by 45 minutes instead of 30, what would the new time be?
3. How would the total distance change if the speed reduction was 150 km/h instead of 200 km/h?
4. How long would the flight take if there was no speed reduction?
5. What if the distance was 800 km, how would the new time be affected?

**Tip:** When solving for variables in word problems, always double-check your units and ensure consistency across equations.

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

This problem explores a time-speed-distance scenario involving an aircraft's flight. The problem demonstrates how to solve for the original duration of the flight when the aircraft's speed is reduced by 200 km/h, and the time increases by 30 minutes. The step-by-step solution uses algebra and linear equations, ideal for Grades 8-10 students.

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