Discussion
The speed of stream is 4 km/hr. A boat goes 120 km and comes back to the starting point in 40 hours. What is the speed of the boat in still water?
Answer: B
Let the speed of the boat in still water be v km/hr. Going down the stream the speed is v + 4 and coming back it is v - 4, and the total time is 40 hours.
\[ \frac{120}{v+4} + \frac{120}{v-4} = 40 \]
\[ \frac{240v}{v^{2}-16} = 40 \Rightarrow v^{2} - 6v - 16 = 0 \]
This gives v = 8, so the speed in still water is 8 km/hr, option (B). Speeds of 15 and 10 would take much less than 40 hours. Check: 120 / 12 = 10 hours downstream and 120 / 4 = 30 hours upstream, and 10 + 30 = 40 hours, which agrees with the given time.
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