Calculating Total Duration Away: Time Zone Travel Problem

This solution details the calculation for the total time a person was away from their original place, considering the travel duration and a time zone difference.

1. Outward Journey Analysis

The man departs his original place at 0100 Hrs local time and arrives at the destination at 0900 Hrs local time on the same date.

The destination's time zone lags by 10 hours. This means the destination time is 10 hours behind the original place's time.

Original Place Time = Destination Time + 10 hours

To find the travel duration in the original place's time frame:

Arrival Time (Original Equivalent) = 0900 Hrs (Destination) + 10 hours = 1900 Hrs (Original Place Time).

The travel duration for the outward journey is:

$ \text{Travel Duration} = \text{Arrival Time (Original)} - \text{Departure Time (Original)} $

$ \text{Travel Duration} = 1900 \text{ Hrs} - 0100 \text{ Hrs} = 18 \text{ hours} $

2. Return Journey Analysis

The return journey starts on the same night at 2100 Hrs local time (destination time) and takes the same duration (18 hours).

Convert the return departure time to the original place's time zone:

Departure Time (Return, Original Equivalent) = 2100 Hrs (Destination) + 10 hours

$ 2100 \text{ Hrs} + 10 \text{ hours} = 3100 \text{ hours} $

Since 3100 hours is more than 24 hours, this indicates the start of the next day in the original time zone.

$ 3100 \text{ hours} = 2400 \text{ hours} + 700 \text{ hours} $

So, the departure time for the return journey, referenced to the original place's time zone, is 0700 Hrs on the next day.

3. Calculating Arrival Back Time

The return travel duration is 18 hours.

Arrival Time (Back) = Departure Time (Return, Original) + Return Travel Duration

$ \text{Arrival Time (Back)} = 0700 \text{ Hrs (Day 2)} + 18 \text{ hours} $

$ \text{Arrival Time (Back)} = 2500 \text{ Hrs (Day 2)} $

Converting this to standard time:

$ 2500 \text{ Hrs} = 2400 \text{ Hrs} + 100 \text{ Hrs} $

The man arrives back at his original place at 0100 Hrs on Day 3.

4. Total Time Away

The man departed his original place at 0100 Hrs on Day 1.

He arrived back at his original place at 0100 Hrs on Day 3.

The total duration he was away is the difference between the final arrival time and the initial departure time.

$ \text{Total Time Away} = (\text{0100 Hrs Day 3}) - (\text{0100 Hrs Day 1}) $

$ \text{Total Time Away} = 2 \text{ days} = 48 \text{ hours} $