Train Time Gap 844B5F

1. **State the problem:** We are given train times from Waterloo to Dartford for three different journeys. The total journey time from Waterloo to Dartford is always the same. We need to find the missing time in the gap for the first journey starting at 16:45 from Waterloo. 2. **Identify the total journey time for known journeys:** - For the first journey starting at 16:15, the arrival at Dartford is 17:20. - Total journey time = Arrival time - Departure time = $$17:20 - 16:15$$. 3. **Calculate the total journey time for the first journey:** - Convert times to minutes: - 16:15 = $$16 \times 60 + 15 = 975$$ minutes - 17:20 = $$17 \times 60 + 20 = 1040$$ minutes - Total journey time = $$1040 - 975 = 65$$ minutes 4. **Apply the same total journey time to the second journey starting at 16:45:** - Departure time = 16:45 = $$16 \times 60 + 45 = 1005$$ minutes - Arrival time at Dartford = Departure time + total journey time = $$1005 + 65 = 1070$$ minutes 5. **Convert arrival time back to hours and minutes:** - Hours = $$\lfloor \frac{1070}{60} \rfloor = 17$$ - Minutes = $$1070 \mod 60 = 50$$ - So, arrival time at Dartford = 17:50 6. **Find the missing time at Waterloo for the second journey:** - The gap is the arrival time at the station after Waterloo but before Bridge for the second journey. - Since the total journey time is constant, the missing time is the departure time from Waterloo for the second journey, which is given as 16:45. **Final answer:** The missing time in the gap is **16:45**.