A boat moves at 14 km/hr in still water. Over a 45 km stretch of a river, it takes 2 hours more to go upstream than to go downstream. What is the speed of the stream?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 km/hr
Let the speed of the stream be \(s\) km/hr. The upstream time minus the downstream time is 2 hours, which gives one equation in \(s\).
Upstream speed \(=14-s\), downstream speed \(=14+s\)
\(\displaystyle \frac{45}{14-s}-\frac{45}{14+s}=2\)
\(\displaystyle \frac{45\times2s}{196-s^{2}}=2\), so \(90s=392-2s^{2}\)
\(s^{2}+45s-196=0\), that is \((s+49)(s-4)=0\)
A speed is positive, so \(s=4\) km/hr
Check: \(45\div10=4.5\) hours up and \(45\div18=2.5\) hours down; the difference is 2 hours