Question

Alf headed for the rodeo at 9am at 30 mph. At 11am bubba headed after her at 60 mph. What time was it when una caught up with Alf?

Answer 1

Let's analyze the problem step by step.

1. **Determine how long Alf has been traveling by the time Bubba starts:**
- Alf starts at 9 AM and Bubba starts at 11 AM.
- Therefore, Alf travels for 2 hours before Bubba starts.

2. **Calculate the distance Alf travels in those 2 hours:**
- Speed of Alf = 30 mph
- Time traveled by Alf = 2 hours
- Distance = Speed × Time = 30 mph × 2 hours = 60 miles

3. **Set up the equation for when Bubba catches up to Alf:**
- After 11 AM, let \( t \) be the time in hours that Bubba travels until he catches up with Alf.
- In that time, Alf continues to travel as well.
- Distance traveled by Alf after 11 AM = \( 30 \, \text{mph} \times t \)
- Total distance traveled by Alf = \( 60 + 30t \)
- Distance traveled by Bubba = \( 60 \, \text{mph} \times t \)

4. **Set distances equal to each other to find \( t \):**
\[
60 + 30t = 60t
\]

5. **Solve for \( t \):**
\[
60 = 60t - 30t
\]
\[
60 = 30t
\]
\[
t = 2 \text{ hours}
\]

6. **Determine the time when Bubba catches up with Alf:**
- Bubba started at 11 AM, and it takes him 2 hours to catch up.
- Therefore, he catches up at \( 11 \text{ AM} + 2 \text{ hours} = 1 \text{ PM} \).

Thus, Bubba caught up with Alf at **1 PM**.