A person takes 2.2 times longer to row a certain distance upstream compared to rowing the same distance downstream. If the person can row 55 km downstream in 2 hours and 30 minutes, determine the speed of the boat in still water.

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Accepted Answer

First, let's identify what we know:
- Time ratio (upstream:downstream) = 2.2:1
- Downstream distance = 55 km
- Downstream time = 2.5 hours (2 hours 30 minutes)

Let's find the downstream speed:
Downstream speed = Distance/Time = 55/2.5 = 22 km/h

Let's denote:
- u = speed of boat in still water
- v = speed of stream

**Using the formulas:**
- Downstream speed = u + v = 22 km/h
- Upstream speed = u - v

Since the time ratio for upstream to downstream is 2.2:1, and time is inversely proportional to speed:
Speed ratio (upstream:downstream) = 1:2.2

Therefore:
(u - v)/(u + v) = 1/2.2
(u - v) = (u + v)/2.2
(u - v) = 22/2.2 = 10 km/h

This gives us two equations:
- u + v = 22 km/h
- u - v = 10 km/h

Solving these equations:
Adding both equations: 2u = 32
Therefore, u = 16 km/h

We can verify: v = 22 - 16 = 6 km/h
Speed of boat in still water = 16 km/h

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