Discussion
A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Then the speed of the man in still water and the speed of the current is:
Answer: A
The man rows at 8 km/h in still water and the current is 3 km/h: (8, 3 kmph).
Let the upstream speed be u and the downstream speed d. Write a = 1/u and b = 1/d to make the equations linear.
\[ \begin{aligned} 40a + 55b &= 13 \\ 30a + 44b &= 10 \end{aligned} \]
\[ \begin{aligned} 120a + 165b &= 39 \\ 120a + 176b &= 40 \\ 11b &= 1,\ b = \tfrac{1}{11} \end{aligned} \]
Then \(40a = 13 - 5 = 8\), so a = 1/5. The speeds are u = 5 km/h and d = 11 km/h.
\[ \begin{aligned} \text{still water} &= \tfrac{11 + 5}{2} = 8 \\ \text{current} &= \tfrac{11 - 5}{2} = 3 \end{aligned} \]
All options give 8 for the boat, so only the current differs; 4, 3.2 and 3.5 km/h do not satisfy both trips.
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