A boatman rows 2 km upstream in 1 hour and 1 km downstream in 10 minutes. How long will he take to row 5 km in still water?

Given data

• Upstream: 2 km in 1 h ⇒ u − v = 2 km/h
• Downstream: 1 km in 10 min = 1/6 h ⇒ u + v = 6 km/h
• Need time for 5 km in still water (speed = u)

Concept / Approach

• Let u be speed in still water; v be current speed.
• Solve the system for u, then compute time = distance / speed.

Step-by-step calculation

u − v = 2 … (1)u + v = 6 … (2)Adding (1) and (2): 2u = 8 ⇒ u = 4 km/hTime in still water for 5 km = 5 / 4 h = 1.25 h = 1 hour 15 minutes

Verification

v = (6 − 2)/2 = 2 km/h. Upstream speed = 2 km/h and downstream speed = 6 km/h match the data.

Common pitfalls

• Using average of 2 and 6 as time; it is speed that averages (and specifically (up + down)/2 for u).
• Converting 10 minutes incorrectly.

Final Answer

1 hour 15 minutes