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.

Question

What was their speed?

Answer 1

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.

Answer 2

Solve for x.
9 ≤ 17 − 4x

Answer 3

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 \( (-\infty, 2] \).