Discussion
Ajay takes 4 hours more while swimming upstream than downstream. His speed in still water is 10 km/hr. The speed of stream is 2 km/hr. What is the distance?
Answer: A
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 12 \text{ km/h}, \qquad b - r = 8 \text{ km/h} \]
The upstream trip takes 4 hours longer over the same distance \( D \):
\[ \frac{D}{8} - \frac{D}{12} = 4 \]
\[ D\left(\frac{3 - 2}{24}\right) = 4 \quad\Longrightarrow\quad \frac{D}{24} = 4 \]
\[ D = 96 \text{ km} \]
Checking: 12 hours upstream against 8 hours downstream - a difference of exactly 4.
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