A boat covers 18 km downstream in 3 hours. If the speed of the current is $33 \frac{1}{3} \%$ of its downstream speed, in what time will it cover a distance of 100 km upstream?

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**Solution:**

1. Calculate downstream speed:
   - Downstream speed = $ \frac{18}{3} = 6 \text{ km/hr} $
   - Let $ x $ = speed of boat in still water, $ y $ = speed of current.
   - So, $ x + y = 6 $

2. Given speed of current is $ 33 \frac{1}{3} \% = \frac{1}{3} $ of downstream speed:
   - $ y = \frac{1}{3} \times 6 = 2 \text{ km/hr} $

3. Calculate speed of boat in still water:
   - $ x = 6 - 2 = 4 \text{ km/hr} $

4. Calculate upstream speed:
   - Upstream speed = $ x - y = 4 - 2 = 2 \text{ km/hr} $

5. Calculate time to cover 100 km upstream:
   - Time = $ \frac{\text{Distance}}{\text{Speed}} = \frac{100}{2} = 50 \text{ hours} $

**Answer:** 50 hour

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