2015 · Q24
A person goes to a market between 4 p.m. and 5 p.m. When he comes back, he finds that the hour hand and minute hand have interchanged their positions. For how much time (approximately) was he out of his house?
Elementary MathematicsTime, Speed and Distance
- A55.25 minutes
- B55.30 minutes
- C55.34 minutes
- D55.38 minutes
Explanation
For the hands to interchange, departure t₁ and return t₂ (minutes after 4:00) satisfy 6t₂ − 360 = 120 + t₁/2 with t₂ = 12t₁ − 240, giving t₁ ≈ 26.85 and t₂ ≈ 82.24. Time out = t₂ − t₁ = 720/13 ≈ 55.38 minutes (option D).