Question

Clara is going on a hike to the top of a mountain. It will take 3 hours and 15 minutes to hike up the mountain and 57 minutes to hike back down. If Clara wants to finish the hike by 12:55 P.M., what is the latest time she can start the hike up the mountain?

Answer 1

First, we will convert the times for the hike into a single unit (minutes) for easier calculation.

1. **Hiking up the mountain:**
- Time taken: 3 hours and 15 minutes
- Convert to minutes:
\[
3 \text{ hours} = 3 \times 60 = 180 \text{ minutes}
\]
\[
3 \text{ hours and } 15 \text{ minutes} = 180 \text{ minutes} + 15 \text{ minutes} = 195 \text{ minutes}
\]

2. **Hiking down the mountain:**
- Time taken: 57 minutes

3. **Total time for the hike:**
- Combine the time to hike up and down:
\[
\text{Total time} = 195 \text{ minutes} + 57 \text{ minutes} = 252 \text{ minutes}
\]

4. **Convert the total hiking time back into hours and minutes:**
- 252 minutes to hours:
\[
252 \div 60 = 4 \text{ hours and } 12 \text{ minutes}
\]

5. **Determine the finish time:**
- Clara wants to finish the hike by 12:55 P.M.
- To find the latest start time, we subtract the total hiking time from the finish time:
\[
12:55 \text{ P.M.} - 4 \text{ hours and } 12 \text{ minutes}
\]

Start by subtracting the hours:
- 12:55 P.M. - 4 hours = 8:55 A.M.

Now subtract the minutes:
- 8:55 A.M. - 12 minutes = 8:43 A.M.

Thus, the latest time Clara can start her hike up the mountain is **8:43 A.M.**