A hot air balloon flying at a speed of 18 km/hr travelled 12 km. During its return journey, the balloon took 1 hour against the wind to reach origin, find the speed of the wind?

To find the speed of the wind, let's break down the problem:

### Given Data:
- Speed of the balloon in still air (without wind) = 18 km/h
- Distance traveled by the balloon = 12 km
- Time taken for the return journey = 1 hour

### Approach:

1. **Calculate the effective speed during the return journey:**
   - Let the speed of the wind be \( w \) km/h.
   - During the return journey, the balloon is flying against the wind, so the effective speed of the balloon will be reduced by the speed of the wind.
   - Therefore, the effective speed of the balloon during the return journey = \( 18 \, \text{km/h} - w \, \text{km/h} \).

2. **Use the distance-time relationship for the return journey:**
   - The time taken for the return journey is 1 hour.
   - The distance traveled during the return journey is 12 km.
   - Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \), we get:
     \[
     1 \, \text{hour} = \frac{12 \, \text{km}}{18 \, \text{km/h} - w \, \text{km/h}}
     \]

3. **Solve for \( w \):**
   \[
   18 \, \text{km/h} - w \, \text{km/h} = 12 \, \text{km}
   \]
   \[
   18 - w = 12
   \]
   \[
   w = 18 - 12 = 6 \, \text{km/h}
   \]

### Conclusion:
The speed of the wind is 6 km/h.

Would you like any further details or have any questions? Here are some related questions:

1. How long would the return journey take if the wind speed increased to 8 km/h?
2. What would the total time be for the round trip in the presence of a 6 km/h wind?
3. If the distance for the outward journey was 15 km, what would be the new wind speed given the same return time?
4. How would the return time change if the wind speed was reduced by half?
5. What would the speed of the balloon need to be to maintain a 1-hour return journey if the wind speed increased to 10 km/h?

**Tip:** When dealing with problems involving wind speed or current speed, always account for the direction of the wind/current in relation to the object's movement.

Learn how to calculate the speed of the wind in a hot air balloon problem. Given the balloon's speed and travel distance, find the wind speed using basic speed, distance, and time equations. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation