A boat can row to a place 56 km away and return in 22 hours. The time taken to row 21 km downstream is equal to the time taken to row 12 km upstream. What is the speed of the boat in still water?

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Accepted Answer

**Solution:**

1. Let the speed of the boat in still water be *b* kmph and the speed of the stream be *s* kmph.

2. Speed downstream = *(b + s)* kmph, speed upstream = *(b - s)* kmph.

3. Given that the time taken to row 21 km downstream equals the time taken to row 12 km upstream:
   
   $$\frac{21}{b + s} = \frac{12}{b - s}$$

4. Cross-multiplying:
   
   $$21(b - s) = 12(b + s)$$

$$21b - 21s = 12b + 12s$$

$$21b - 12b = 21s + 12s$$

$$9b = 33s$$

$$s = \frac{9b}{33} = \frac{3b}{11}$$

5. The total time for the round trip of 56 km each way is 22 hours:
   
   $$\frac{56}{b + s} + \frac{56}{b - s} = 22$$

6. Substitute *s = \frac{3b}{11}*:
   
   $$\frac{56}{b + \frac{3b}{11}} + \frac{56}{b - \frac{3b}{11}} = 22$$

$$\frac{56}{b(1 + \frac{3}{11})} + \frac{56}{b(1 - \frac{3}{11})} = 22$$

$$\frac{56}{b 	imes \frac{14}{11}} + \frac{56}{b 	imes \frac{8}{11}} = 22$$

$$\frac{56 	imes 11}{14b} + \frac{56 	imes 11}{8b} = 22$$

$$\frac{616}{14b} + \frac{616}{8b} = 22$$

$$\frac{44}{b} + \frac{77}{b} = 22$$

$$\frac{121}{b} = 22$$

7. Solving for *b*:
   
   $$b = \frac{121}{22} = 5.5 	ext{ kmph}$$

**Answer:** $5.5 	ext{ kmph}$

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