A man can row at 6 km/h in still water. When the river is running at 1.2 km/h, it takes him a total of 1 hour to row from one point to another and then back to the starting point. What is the total distance travelled by the man (in km)?

Introduction / Context:
This question asks you to find the total distance travelled in a round trip on a river, given the boat's speed in still water, the speed of the current, and the total time taken for going and returning. It is a typical boats and streams problem that uses relative speeds and time calculations.

Given Data / Assumptions:

Boat speed in still water, b = 6 km/h.
River current speed, c = 1.2 km/h.
Downstream speed = b + c = 6 + 1.2 = 7.2 km/h.
Upstream speed = b - c = 6 - 1.2 = 4.8 km/h.
Let the one-way distance between the two points be d km.
Total time for going downstream and returning upstream = 1 hour.
We are asked for the total distance travelled, which is 2d.

Concept / Approach:
Time is distance divided by speed. The total time is the sum of the time downstream and the time upstream. We create an equation with d as the unknown: d/7.2 + d/4.8 = 1. Solving for d yields the one-way distance, and doubling it gives the total distance travelled.

Step-by-Step Solution:
Step 1: Write the time equation. Downstream time = d / 7.2 hours. Upstream time = d / 4.8 hours. Total time: d/7.2 + d/4.8 = 1. Step 2: Simplify by using fractions for speeds. 7.2 = 36/5, so d/7.2 = d / (36/5) = 5d/36. 4.8 = 24/5, so d/4.8 = d / (24/5) = 5d/24. Thus 5d/36 + 5d/24 = 1. Step 3: Combine the fractions. Factor out 5d: 5d(1/36 + 1/24) = 1. 1/36 + 1/24 = (2 + 3) / 72 = 5 / 72. So 5d * (5/72) = 1 ⇒ 25d / 72 = 1. d = 72 / 25 = 2.88 km (one way). Step 4: Compute total distance. Total distance = 2d = 2 * 2.88 = 5.76 km.

Verification / Alternative check:
Check time with d = 2.88 km. Downstream time = 2.88 / 7.2 = 0.4 h (24 minutes). Upstream time = 2.88 / 4.8 = 0.6 h (36 minutes). Total = 0.4 + 0.6 = 1 hour, which matches the given total time exactly. Thus 5.76 km is correct.

Why Other Options Are Wrong:
4.58 km, 5.24 km or 6.35 km would give total times that are not equal to 1 hour when you recompute downstream and upstream times with speeds 7.2 km/h and 4.8 km/h.

Common Pitfalls:
Some students incorrectly assume that the average speed for the round trip is simply the average of 7.2 and 4.8, which is not valid when time in each direction is unknown. Others make arithmetic mistakes converting decimal speeds to fractions. Always solve for distance using the time equation and double-check by substituting back into the problem.

Final Answer:
The total distance travelled by the man is 5.76 km.