The speed of a boat in still water is 4 times the speed of the stream. Over a 45 km stretch of the river, the boat takes 1 hour more to go upstream than to go downstream. What is the speed of the stream?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 km/hr
Let the speed of the stream be \(s\) km/hr; the boat’s speed is then \(4s\). Both trip speeds are written in \(s\), and the upstream time minus the downstream time is 1 hour.
Downstream speed \(=4s+s=5s\), upstream speed \(=4s-s=3s\)
\(\displaystyle \frac{45}{3s}-\frac{45}{5s}=1\)
\(\displaystyle \frac{15}{s}-\frac{9}{s}=\frac{6}{s}=1\), so \(s=6\) km/hr
Check: boat \(=24\) km/hr; \(45\div18=2.5\) hours up and \(45\div30=1.5\) hours down; the difference is 1 hour