A man can row at 6 km/h in still water. The river flows at 1.2 km/h. It takes him a total of 1 hour to row from his starting point to a place and then return. What is the total distance he travels (in km)?

Introduction / Context:
This question involves a boat travelling in a river where there is a current. The speed of the boat in still water and the speed of the stream are known, and the total time for a round trip is given. We are asked to compute the total distance covered. The idea is to work out the downstream and upstream speeds, express the one way distance as a variable, and then use the total time equation to find that distance and hence the round trip distance.

Given Data / Assumptions:

• Speed of boat in still water = 6 km/h.
• Speed of river current = 1.2 km/h.
• Total time for going to the destination and coming back = 1 hour.
• The distance between the two points is the same in both directions.
• We assume uniform speeds throughout the motion.

Concept / Approach:
When a boat moves with the current, its effective speed is boat speed plus stream speed. When it moves against the current, its effective speed is boat speed minus stream speed. If the one way distance is d km, the total time is d divided by downstream speed plus d divided by upstream speed. This total is given as 1 hour, which allows us to solve for d and hence find the total distance 2d.

Step-by-Step Solution:
Let d be the distance (in km) from the starting point to the place. Downstream speed = 6 + 1.2 = 7.2 km/h. Upstream speed = 6 - 1.2 = 4.8 km/h. Time downstream = d / 7.2 hours. Time upstream = d / 4.8 hours. Total time = d / 7.2 + d / 4.8 = 1 hour. Compute d / 7.2 + d / 4.8 = 1. Take common denominator: 7.2 * 4.8. This simplifies to d * (4.8 + 7.2) / (7.2 * 4.8) = 1. So d * 12 / (34.56) = 1 giving d = 34.56 / 12 = 2.88 km. Total distance travelled = 2d = 2 * 2.88 = 5.76 km.

Verification / Alternative check:
Using d = 2.88 km, time downstream is 2.88 / 7.2 = 0.4 hours (24 minutes). Time upstream is 2.88 / 4.8 = 0.6 hours (36 minutes). The sum 0.4 + 0.6 = 1 hour matches the given total time. Therefore the distance calculation is correct and the total distance travelled is 5.76 km.

Why Other Options Are Wrong:
A total distance of 4.58 km or 5.24 km would produce total times different from 1 hour when substituted into the same calculation. A distance of 6.35 km would also result in a longer total time because the speeds are fixed and the distance is larger. Only 5.76 km makes the downstream and upstream times sum to the given 1 hour.

Common Pitfalls:
Students sometimes confuse total distance with one way distance, mistakenly using d instead of 2d. Another common mistake is to directly average the speeds instead of correctly using time = distance / speed for each leg of the journey. Forgetting to add and subtract the current speed correctly also leads to errors. Careful use of the formulas is important to avoid those traps.

Final Answer:
The man travels a total distance of 5.76 km during the round trip.