A man can row at 8 km/h in still water. The river current flows at 2 km/h. For the same distance, it takes him 4 hours longer to row upstream than to row downstream. What is that distance (in km)?

Introduction / Context:
This problem is about comparing the time taken to travel the same distance upstream and downstream when both the boat speed and stream speed are known. We are told that the upstream journey takes 4 hours more than the downstream journey, and we need to find the common distance. Such questions require forming equations using the basic relation time = distance / speed for both directions.

Given Data / Assumptions:

• Boat speed in still water = 8 km/h.
• River current speed = 2 km/h.
• Distance covered upstream and downstream is the same (call it d km).
• Upstream journey takes 4 hours more than downstream journey.
• Speeds and current are uniform.

Concept / Approach:
The effective speeds are:

• Downstream speed = boat speed + current = 8 + 2 = 10 km/h.
• Upstream speed = boat speed - current = 8 - 2 = 6 km/h.

If the distance is d km, time downstream is d / 10 hours and time upstream is d / 6 hours. The difference between these times is 4 hours. This leads to a simple linear equation in d that we can solve to obtain the distance.

Step-by-Step Solution:
Let the distance be d km. Downstream speed = 10 km/h, upstream speed = 6 km/h. Downstream time = d / 10 hours. Upstream time = d / 6 hours. Given that upstream time is 4 hours more: d / 6 - d / 10 = 4. Find a common denominator: 30. Then (5d - 3d) / 30 = 4, so 2d / 30 = 4. Simplify to d / 15 = 4, thus d = 4 * 15 = 60 km.

Verification / Alternative check:
If the distance is 60 km, downstream time is 60 / 10 = 6 hours. Upstream time is 60 / 6 = 10 hours. The difference 10 - 6 = 4 hours matches the given condition. So the calculated distance 60 km is consistent with all the data and is therefore correct.

Why Other Options Are Wrong:
For 32 km, the times would be 3.2 hours downstream and about 5.33 hours upstream, a difference of only 2.13 hours. For 45 km, the times would be 4.5 hours and 7.5 hours, a difference of 3 hours. For 54 km, the difference is 3.6 hours. None of these match the required 4 hour difference. Only 60 km gives exactly a 4 hour difference between upstream and downstream travel times.

Common Pitfalls:
A frequent error is to subtract the speeds first and incorrectly think that time difference is distance divided by speed difference. That approach does not correctly reflect the relation between time, distance, and speed in each direction. Another pitfall is misreading the statement and treating 4 hours as the total time rather than the difference in times. Setting up the equation d / 6 - d / 10 = 4 is the key step to solving such problems correctly.

Final Answer:
The distance for which the upstream time is 4 hours more than the downstream time is 60 km.