Question

Rogelio's watch stopped at 2:00 p.m. He started it without changing the time and went to visit a friend. When he arrived, he was told that it was 4:10 p.m. He stayed with his friend for exactly two hours and walked back home, taking the same amount of time as he had left. He went to the clock, which at that moment read 4:40 p.m., and set it to the correct time. How could he have known? Rogelio, what was the exact time? What was the exact time?

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Neal

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89 Answers

1. Let \( t \) be the time taken to walk from Rogelio's home to his friend's house.

2. Rogelio's journey: \( \text{Left home at 2:00 p.m.} \)

3. Rogelio's friend told him the correct time was 4:10 p.m. after arriving.

2:00 \, \text{p.m.} + t = 4:10 \, \text{p.m.}

4. Determine \( t \):

t = 4:10 \, \text{p.m.} - 2:00 \, \text{p.m.}

t = 2 \, \text{h} \, 10 \, \text{min}

5. Rogelio stayed for 2 hours:

\text{Leave friend's house at 4:10 p.m.} + 2 \, \text{h} = 6:10 \, \text{p.m.}

6. Walk home taking \( t \) time:

6:10 \, \text{p.m.} + 2 \, \text{h} \, 10 \, \text{min} = 8:20 \, \text{p.m.}

7. On arriving, Rogelio's watch reads 4:40 p.m. but needs setting to correct time:

\text{Current time display} + (\text{correct time difference})

4:40 \, \text{p.m.} + 10 \, \text{min} = 4:50 \, \text{p.m.}

8. Exact time is:

5:10 \, \text{p.m.}

2. Rogelio's journey: \( \text{Left home at 2:00 p.m.} \)

3. Rogelio's friend told him the correct time was 4:10 p.m. after arriving.

4. Determine \( t \):

5. Rogelio stayed for 2 hours:

6. Walk home taking \( t \) time:

7. On arriving, Rogelio's watch reads 4:40 p.m. but needs setting to correct time:

8. Exact time is:

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