Asked by Bornana
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?
What was their speed?
Answers
Answered by
Bornana
Solve for x.
9 ≤ 17 − 4x
9 ≤ 17 − 4x
Answered by
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.
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.
Answered by
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 \( (-\infty, 2] \).
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 \( (-\infty, 2] \).
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