A car travels at 110 km/h for **half the distance** to a town and then travels at 80.0 km/h for the other **half of the distance**.  If the trip took 3.00 h, how far is it to the town?

Let the total distance to the town be \( D \). Then, each half of the distance is \( \frac{D}{2} \).

1. **Time for the first half**: 
   \[
   t_1 = \frac{\frac{D}{2}}{110} = \frac{D}{220}
   \]

2. **Time for the second half**: 
   \[
   t_2 = \frac{\frac{D}{2}}{80} = \frac{D}{160}
   \]

3. **Total time**: 
   \[
   t_1 + t_2 = 3 \quad \Rightarrow \quad \frac{D}{220} + \frac{D}{160} = 3
   \]

To solve this equation, find a common denominator (which is 880):
\[
\frac{4D}{880} + \frac{5.5D}{880} = 3
\]
\[
\frac{9.5D}{880} = 3
\]

Now, multiply both sides by 880:
\[
9.5D = 2640
\]
\[
D = \frac{2640}{9.5} \approx 277.89 \text{ km}
\]

Thus, the distance to the town is approximately **277.89 km**.

Would you like more details on this solution or have any questions? Here are some related questions to consider:

1. How does the average speed of the entire trip compare to the speeds of each segment?
2. What would happen if the car traveled at the same speed for the entire distance?
3. How would the time change if the speed for the first half was increased?
4. What is the impact of distance on travel time at different speeds?
5. How would the result change if the second half was traveled at a higher speed than the first? 

Tip: To solve problems involving distances and speeds, always break the journey into segments based on speed changes.

A car travels at 110 km/h for half the distance to a town and then travels at 80.0 km/h for the other half of the distance. If the trip took 3.00 h, how far is it to the town?

Discover how to calculate the distance to a town when a car travels at different speeds. This problem illustrates the use of the distance formula, with the car traveling 110 km/h and 80 km/h, taking a total of 3 hours. The solution reveals the total distance is approximately 277.89 km.

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