A boatman can row 96 km downstream in 8 hours. If the speed of the current is 4 km/h, in how much time (in hours) will he cover 8 km upstream?

Introduction / Context:
This question checks your understanding of how to use downstream information to find the speed of a boat in still water and then use that to compute an upstream journey time. It connects distance, speed, and time with the influence of river current on rowing speed.

Given Data / Assumptions:
- Downstream distance = 96 km. - Time taken downstream = 8 hours. - Speed of current = 4 km/h. - Required: time to cover 8 km upstream. - Let b be the speed of the boat in still water (km/h).

Concept / Approach:
First find the downstream speed using distance / time. Since downstream speed equals b + c, where c is current speed, you can find b. Then upstream speed equals b - c. Finally, use time = distance / speed to calculate how long it takes to go 8 km upstream. This sequence is typical in many boat and stream problems.

Step-by-Step Solution:
Step 1: Downstream speed = 96 / 8 = 12 km/h. Step 2: Let b be the boat speed in still water and c = 4 km/h be the current speed. Step 3: b + c = downstream speed, so b + 4 = 12. Step 4: Solve for b: b = 12 - 4 = 8 km/h. Step 5: Upstream speed = b - c = 8 - 4 = 4 km/h. Step 6: Required upstream distance = 8 km. Step 7: Time upstream = distance / upstream speed = 8 / 4 = 2 hours.

Verification / Alternative check:
Check consistency: with b = 8 km/h and c = 4 km/h, downstream speed is 8 + 4 = 12 km/h, giving time 96 / 12 = 8 hours as in the question. Upstream speed is 8 - 4 = 4 km/h; at this speed, in 2 hours the boat covers 2 * 4 = 8 km. The calculations match the problem statement perfectly.

Why Other Options Are Wrong:
- 1 hour would correspond to an unrealistic upstream speed of 8 km/h, which would not match the still water speed found from downstream data. - 1.5 hours or 2.5 hours both represent incorrect divisions of 8 by the upstream speed. - 3 hours is much too long and would imply a very low upstream speed that conflicts with the given scenario.

Common Pitfalls:
Learners may mistakenly use the downstream speed directly for upstream travel or subtract the current from the distance instead of the speed. Others forget to separate the steps: first find boat speed in still water, then find upstream speed, and only then calculate time. Keeping a clear step order avoids confusion.

Final Answer:
The boatman will take 2 hours to cover 8 km upstream.