an aircraft carrier made a trip to guam and back. the trip there took three hours and the trip back took four hours. it averaged 6 km/h on the return trip. find the average speed of the trip there.

Let's break down the problem to solve for the average speed of the trip to Guam.

### Step 1: Define Variables
- Let the distance from the starting point to Guam be \( d \) kilometers.
- Let the average speed for the trip to Guam be \( v \) km/h.

### Step 2: Use the Information Given
- Time taken for the trip to Guam = 3 hours.
- Time taken for the return trip = 4 hours.
- Average speed on the return trip = 6 km/h.

### Step 3: Write the Equations
1. For the return trip:
   \[
   \text{Distance} = \text{Speed} \times \text{Time} \Rightarrow d = 6 \times 4 = 24 \text{ km}
   \]
   So, the distance to Guam \( d \) is 24 km.

2. For the trip to Guam:
   \[
   \text{Speed} = \frac{\text{Distance}}{\text{Time}} \Rightarrow v = \frac{d}{3}
   \]

### Step 4: Substitute the Known Distance
Substitute \( d = 24 \) km into the equation for \( v \):
\[
v = \frac{24}{3} = 8 \text{ km/h}
\]

### Conclusion:
The average speed of the trip to Guam was **8 km/h**.

Would you like further details or have any questions? 

Here are some related questions to explore:
1. How would the average speed change if the trip back took 5 hours instead of 4?
2. What would be the total travel time for both trips?
3. How does the average speed for the entire journey compare to the individual speeds?
4. If the distance were doubled, how would that affect the travel times?
5. What if the aircraft carrier had a different speed each hour? How would we calculate the average speed then?

**Tip:** Understanding how to set up equations from word problems is crucial in solving physics and math problems involving rates, speeds, and distances.

Learn how to calculate the average speed of an aircraft carrier trip to Guam. Understand the relationship between speed, distance, and time with a step-by-step solution. Suitable for Grades 7-9.

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