 Audric drove 120 km from Quezon City to San Pablo, Laguna to attend their family reunion. His average speed for the trip to San Pablo, Laguna was 10 km/h faster than on the way back to Quezon City, and as a result, his return trip took an hour longer. What is his average speed in the trip to San Pablo, Laguna?
Construct a table for the quantities based on the given information 

To solve the problem and construct a table based on the given information, we can use the formula:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

Let \( x \) be Audric's average speed on the trip back to Quezon City (in km/h). According to the problem:
- His average speed on the trip to San Pablo, Laguna is \( x + 10 \) km/h.
- The distance for both trips is the same: 120 km.
- The time for the return trip is 1 hour longer than the trip to San Pablo, Laguna.

Using these, we can construct the table as follows:

### Table for Quantities

| **Trip**                 | **Distance (km)** | **Speed (km/h)**  | **Time (hours)**                        |
|--------------------------|-------------------|-------------------|-----------------------------------------|
| **To San Pablo, Laguna**  | 120               | \( x + 10 \)      | \( \frac{120}{x + 10} \)               |
| **Back to Quezon City**   | 120               | \( x \)           | \( \frac{120}{x} \)                    |

### Equations:
The time difference between the return trip and the trip to San Pablo is given as 1 hour. This leads to the equation:

\[
\frac{120}{x} = \frac{120}{x + 10} + 1
\]

Now let's solve this equation step-by-step:

### Step 1: Clear the fractions by multiplying through by \( x(x + 10) \).

\[
120(x + 10) = 120x + x(x + 10)
\]

Simplifying this will give us the average speed on the trip to San Pablo.

Would you like me to proceed with solving it and explain the steps in more detail?

Audric drove 120 km from Quezon City to San Pablo, Laguna to attend their family reunion. His average speed for the trip to San Pablo, Laguna was 10 km/h faster than on the way back to Quezon City, and as a result, his return trip took an hour longer. What is his average speed in the trip to San Pablo, Laguna?

Solve a real-world distance-speed-time problem: Audric's trip from Quezon City to San Pablo, Laguna. Learn how to calculate the average speed using algebraic methods, and understand the relationship between speed, time, and distance. Suitable for Grades 8-10.

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