Discussion
In 10 hours Mayur rows 30 kms upstream and 44 kms downstream. Also he travels 40 kms upstream and 55 kms downstream in 13 hours. What is speed of the boat in still water?
Answer: B
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Substituting \( x = \dfrac{1}{b-r} \) and \( y = \dfrac{1}{b+r} \) makes both conditions linear:
\[ 30x + 44y = 10, \qquad 40x + 55y = 13 \]
Multiply the first by 4 and the second by 3:
\[ 120x + 176y = 40, \qquad 120x + 165y = 39 \]
\[ 11y = 1 \quad\Longrightarrow\quad y = \frac{1}{11} \quad\Longrightarrow\quad b + r = 11 \]
\[ 30x + 4 = 10 \quad\Longrightarrow\quad x = \frac{1}{5} \quad\Longrightarrow\quad b - r = 5 \]
\[ b = \frac{11 + 5}{2} = 8 \text{ km/h} \]
The reciprocal substitution is the standard move for these paired-journey problems: without it the equations are non-linear and far harder to solve.
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