A boat’s speed in still water is 5 km/h and the river flows at 2 km/h. For the same distance upstream and downstream, the upstream time exceeds the downstream time by 2 hours. Find that distance (in km).

Introduction / Context:
Time difference between upstream and downstream over the same distance allows solving for the distance using b ± c speeds.

Given Data / Assumptions:

• b = 5 km/h; c = 2 km/h
• Upstream speed vu = 3 km/h
• Downstream speed vd = 7 km/h
• Let distance = d km
• Time difference = d/vu − d/vd = 2 h

Concept / Approach:
Form the linear equation in d and solve.

Step-by-Step Solution:

Verification / Alternative check:
Up time = 10.5/3 = 3.5 h; down time = 10.5/7 = 1.5 h; difference = 2 h, as required.

Why Other Options Are Wrong:
Other distances do not yield exactly a 2-hour difference using 3 km/h and 7 km/h.

Common Pitfalls:
Taking the difference of speeds and dividing distance by it. Time difference is not distance divided by speed difference; use the proper fractional relation.

Final Answer:
10.5 km.