Kapil rows in still water at speed u and the river has current speed v. For 12 miles, downstream time is 6 hours less than upstream time. If Kapil could double his still water speed for a 24 mile round trip, downstream time would then be only 1 hour less than upstream time. What is the river current speed?

Introduction / Context:This is a two condition system on upstream and downstream times. First, for usual speed u, 12 miles upstream minus downstream time equals 6 hours. Second, if still water speed doubles to 2u, the time difference shrinks to 1 hour for the same 12 mile leg. We solve for the current v.

Given Data / Assumptions:

• Usual still water speed = u mile/h; current = v mile/h.
• Distances per leg = 12 miles.
• Condition 1: 12 / (u - v) - 12 / (u + v) = 6.
• Condition 2: 12 / (2u - v) - 12 / (2u + v) = 1.

Concept / Approach:Set up the two equations and solve simultaneously for positive u and v. The algebra produces a clean exact solution for v in fractional miles per hour.

Step-by-Step Solution:

Verification / Alternative check:Plug v = 8/3 and the given u value back into Equations A and B; each side balances numerically, confirming consistency.

Why Other Options Are Wrong:Values such as 3 or 4 mile/h violate one or both equations. 10/3 mile/h overstates the current and does not meet the second time difference.

Common Pitfalls:Subtracting times in the wrong order or replacing u with downstream speed. Remember u is still water speed, not downstream speed.

Final Answer:8/3 mile/h