Boat A covers a certain distance downstream and upstream in a total of 27 hours. The downstream speeds of boats A and B are 15 km/hr and 10 km/hr respectively, while their upstream speeds are 12 km/hr and 9 km/hr respectively. What is the total time taken by boat B to cover the same distance downstream and upstream?

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**Solution:**

1. Let the distance traveled downstream (and upstream) be *d* km.

2. For boat A, the total time taken downstream and upstream is given as 27 hours:
   
   $$\frac{d}{15} + \frac{d}{12} = 27$$

3. Find a common denominator and simplify:

$$\frac{4d}{60} + \frac{5d}{60} = 27 \implies \frac{9d}{60} = 27$$

4. Multiply both sides by 60:

$$9d = 27 	imes 60 = 1620$$

5. Divide both sides by 9:

$$d = \frac{1620}{9} = 180 	ext{ km}$$

6. Now, calculate the total time taken by boat B to cover the same distance downstream and upstream:

$$	ext{Time} = \frac{180}{9} + \frac{180}{10} = 20 + 18 = 38 	ext{ hours}$$

**Answer:** 38

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