1, 
A bus is traveling at 50 mph. If the rate of speed increases 3 mph each hour, how long will it be before the bus is traveling at a rate of 80 mph? 2,
Name the rule for this sequence.

18, 14, 10, 6, 2,…

### Problem 1: Bus Speed
The bus starts at 50 mph and increases its speed by 3 mph each hour. We need to find how long it will take for the bus to reach 80 mph.

**Solution:**

1. The initial speed of the bus is 50 mph.
2. The final speed is 80 mph.
3. The rate of increase per hour is 3 mph.

The difference in speed is:
\[
80 \, \text{mph} - 50 \, \text{mph} = 30 \, \text{mph}
\]

The time required to reach this speed is:
\[
\text{Time} = \frac{\text{Difference in speed}}{\text{Rate of increase}} = \frac{30 \, \text{mph}}{3 \, \text{mph per hour}} = 10 \, \text{hours}
\]

So, it will take **10 hours** for the bus to reach 80 mph.

### Problem 2: Sequence Rule
The sequence given is 18, 14, 10, 6, 2,…

**Solution:**

To find the rule, observe the pattern in the differences between consecutive terms:

- \(14 - 18 = -4\)
- \(10 - 14 = -4\)
- \(6 - 10 = -4\)
- \(2 - 6 = -4\)

Each term decreases by 4 from the previous one. This sequence is an **arithmetic sequence** with a common difference of \(-4\).

**Rule:** The sequence follows the rule \( a_n = 18 + (n-1)(-4) \), where \( a_n \) is the \(n\)th term of the sequence.

Would you like more details on any of these solutions or have any other questions? 

### Related Questions:
1. What would be the speed of the bus after 5 hours?
2. If the bus continues to increase its speed, when will it reach 100 mph?
3. What is the general formula to find the speed of the bus after \( n \) hours?
4. What is the 10th term in the sequence you provided?
5. How would the sequence change if the difference was \(-5\) instead of \(-4\)?

**Tip:** For arithmetic sequences, always look for the common difference between terms to identify the pattern.

Learn how to calculate the time it takes for a bus to increase its speed from 50 mph to 80 mph, and discover the rule for the arithmetic sequence 18, 14, 10, 6, 2,.... This page provides detailed solutions and explanations suitable for Grades 7-9.

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