Question

At 3:00 p.m., Jamie leaves her house and drives north to the beach. She arrives at 5:30 p.m. Also leaving at 3:00 p.m., her brother Raul leaves her house and drives south to a state park. He arrives at 4:30 p.m. The driving distance from the beach to the state park is 240 mi. Jamie and Raul drove at the same speed.

What was their speed?

Answers

GPT-4o mini
To find Jamie and Raul's speed, we first need to determine how long each of them drove.

1. **Calculating Jamie's driving time:**
- Jamie leaves at 3:00 p.m. and arrives at 5:30 p.m.
- Total driving time for Jamie = 5:30 p.m. - 3:00 p.m. = 2 hours 30 minutes = \(2.5\) hours.

2. **Calculating Raul's driving time:**
- Raul leaves at 3:00 p.m. and arrives at 4:30 p.m.
- Total driving time for Raul = 4:30 p.m. - 3:00 p.m. = 1 hour 30 minutes = \(1.5\) hours.

3. **There's a direct relationship between the distances traveled by Jamie and Raul:**
- Let the speed of both Jamie and Raul be \(s\) (in miles per hour).
- Distance traveled by Jamie to the beach = \(s \times 2.5\) miles.
- Distance traveled by Raul to the state park = \(s \times 1.5\) miles.

4. **Since the distance between the beach and the state park is given as 240 miles, we can express this relationship as:**
\[
\text{Distance traveled by Jamie} + \text{Distance traveled by Raul} = 240 \text{ miles}
\]
\[
(s \times 2.5) + (s \times 1.5) = 240
\]

5. **Combining the terms yields:**
\[
2.5s + 1.5s = 240
\]
\[
4s = 240
\]

6. **Solving for \(s\):**
\[
s = \frac{240}{4} = 60 \text{ miles per hour}
\]

Thus, Jamie and Raul's speed was \( \boxed{60} \) miles per hour.
Bornana
Solve for x.
9 ≤ 17 − 4x
GPT-4o mini
To solve the inequality \( 9 \leq 17 - 4x \), we'll isolate \( x \).

1. Subtract 17 from both sides:
\[
9 - 17 \leq -4x
\]
\[
-8 \leq -4x
\]

2. Now, divide both sides by -4. Remember, when dividing by a negative number, we must flip the inequality sign:
\[
\frac{-8}{-4} \geq x
\]
\[
2 \geq x
\]

3. This can also be written as:
\[
x \leq 2
\]

Thus, the solution to the inequality is \( x \leq 2 \). We can also express this in interval notation as \( (-\infty, 2] \).