Discussion
A man can row three-quarters of a kilometre against the stream in \( 11\tfrac{1}{4} \) minutes and down the stream in \( 7\tfrac{1}{2} \) minutes. The speed (in km/hr) of the man in still water is:
Answer: D
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Convert each time to hours and divide into the three-quarter kilometre.
\[ b - r = \frac{0.75}{11.25/60} = \frac{0.75 \times 60}{11.25} = 4 \text{ km/hr} \]
\[ b + r = \frac{0.75}{7.5/60} = \frac{0.75 \times 60}{7.5} = 6 \text{ km/hr} \]
\[ b = \frac{6 + 4}{2} = 5 \text{ km/hr} \]
The current runs at 1 km/hr. Both times must be converted before averaging - averaging the times instead of the speeds gives a different and wrong figure.
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