A boat moves at 13 km/hr in still water. Over an 80 km stretch of a river, it takes 3 hours more to go upstream than to go downstream. What is the speed of the stream?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3 km/hr
The stream slows the boat upstream and speeds it up downstream; the upstream time minus the downstream time is 3 hours.
Let the speed of the stream be \(s\) km/hr
\(\displaystyle \frac{80}{13-s}-\frac{80}{13+s}=3\)
\(\displaystyle \frac{80(13+s)-80(13-s)}{169-s^{2}}=\frac{160s}{169-s^{2}}=3\)
\(160s=507-3s^{2}\), that is \(3s^{2}+160s-507=0\)
\((s-3)(3s+169)=0\); a speed is positive, so \(s=3\) km/hr
Check: \(80\div10=8\) hr upstream and \(80\div16=5\) hr downstream; the difference is 3 hr