The speed of a stream is 3 km/h. A boat takes 3 hours more to go 36 km upstream than to go 36 km downstream. What is the speed of the boat in still water?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9 km/h
Let the speed of the boat in still water be \(x\) km/h, so the upstream speed is \(x - 3\) and the downstream speed is \(x + 3\). The upstream time exceeds the downstream time by 3 hours:
\(\displaystyle \frac{36}{x - 3} - \frac{36}{x + 3} = 3\)
\(\displaystyle \frac{36(x + 3) - 36(x - 3)}{x^{2} - 9} = 3\)
\(216 = 3(x^{2} - 9)\)
\(x^{2} = 81\)
\(x = 9\) (speed is positive)
Check: upstream \(36 \div 6 = 6\) hours, downstream \(36 \div 12 = 3\) hours, a difference of 3 hours.
Why the other options are incorrect
Option (1) 6 km/h — Incorrect. The times would be \(36 \div 3 = 12\) and \(36 \div 9 = 4\) hours, a difference of 8 hours.
Option (3) 12 km/h — Incorrect. The times would be \(36 \div 9 = 4\) and \(36 \div 15 = 2.4\) hours, a difference of 1.6 hours.
Option (4) 15 km/h — Incorrect. The times would be \(36 \div 12 = 3\) and \(36 \div 18 = 2\) hours, a difference of 1 hour.