Travel Time Calculation with Time Zones

This problem involves calculating the total duration a man was away from his original place, considering different local times and a significant time zone lag.

Let's denote the man's original country as Country A and the country he visited as Country B.

We are given the following information:

• Departure from Country A: \(0100 \text{ hrs}\) local time (A time) on a certain date.
• Arrival in Country B: \(0900 \text{ hrs}\) local time (B time) on the same date.
• Return journey start from Country B: \(2100 \text{ hrs}\) local time (B time) on the same night.
• Return journey time is the same as the outward journey time.
• Time zone of Country B lags Country A by 10 hours. This means A time = B time + 10 hours, or B time = A time - 10 hours.

Calculating Forward Journey Duration

The man departs A at \(0100 \text{ hrs}\) A time and arrives at B at \(0900 \text{ hrs}\) B time. To find the duration of the journey in A time, we need to convert the arrival time in B to its equivalent in A time.

Arrival time in B = \(0900 \text{ hrs}\) B time.

Convert B time to A time: A time = B time + 10 hours.

Arrival time in A time = \(0900 \text{ hrs} + 10 \text{ hours} = 1900 \text{ hrs}\) A time on the same date.

Departure time from A = \(0100 \text{ hrs}\) A time.

Duration of forward journey = Arrival time (in A time) - Departure time (in A time)

Duration of forward journey = \(1900 \text{ hrs} - 0100 \text{ hrs} = 18 \text{ hours}\).

Calculating Return Journey Details

The problem states that the return journey takes the same time as the outward journey, which is 18 hours.

The man starts his return journey from B at \(2100 \text{ hrs}\) B time on the same night as he arrived.

First, let's convert the departure time from B to A time.

Departure time from B = \(2100 \text{ hrs}\) B time.

Convert B time to A time: A time = B time + 10 hours.

Departure time in A time = \(2100 \text{ hrs} + 10 \text{ hours} = 3100 \text{ hrs}\).

\(3100 \text{ hrs}\) on a clock means \(2400 \text{ hrs} + 700 \text{ hrs}\), so it is \(0700 \text{ hrs}\) on the next day in Country A.

So, the man departs from Country B at \(0700 \text{ hrs}\) A time on the day following his arrival in B.

Now, let's calculate the arrival time back at Country A.

Departure time from B (in A time) = \(0700 \text{ hrs}\) A time (next day).

Return journey duration = 18 hours.

Arrival time back at A = Departure time from B (in A time) + Return journey duration

Arrival time back at A = \(0700 \text{ hrs} + 18 \text{ hours} = 2500 \text{ hrs}\).

\(2500 \text{ hrs}\) on a clock means \(2400 \text{ hrs} + 100 \text{ hrs}\), so it is \(0100 \text{ hrs}\) on the day after next in Country A.

Calculating Total Duration Away

The man started his journey from Country A at \(0100 \text{ hrs}\) A time on the first day.

He returned to Country A at \(0100 \text{ hrs}\) A time on the day after next.

Let's represent the departure day as Day 1.

• Departure from A: Day 1, \(0100 \text{ hrs}\) A time.
• Arrival back at A: Day 3, \(0100 \text{ hrs}\) A time.

Total duration away from his place is the time difference between his return and departure, measured in A time.

Total duration = (Day 3, \(0100 \text{ hrs}\)) - (Day 1, \(0100 \text{ hrs}\)).

This time difference is exactly 48 hours (2 full days).

Let's summarize the timeline in A time:

The total time elapsed from Day 1, \(0100 \text{ hrs}\) to Day 3, \(0100 \text{ hrs}\) is 48 hours.

Therefore, the duration for which the man was away from his place is 48 hours.