A boat moves at 10 km/hr in still water. It goes downstream for 3 hours, then turns at once and goes upstream for 3 hours. It is now 18 km downstream of its starting point. What is the speed of the stream?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3 km/hr
In equal times the boat’s own speed takes it the same distance down and back up, so the boat ends away from the start only because of the stream. The stream adds 3 hours of its speed going down and takes away 3 hours of its speed coming up, so the gap equals 6 hours of the stream’s speed.
Let the speed of the stream be \(s\) km/hr
Downstream in 3 hours: \(3(10+s)\) km
Upstream in 3 hours: \(3(10-s)\) km
\(3(10+s)-3(10-s)=6s=18\), so \(s=3\) km/hr
Check: \(3\times13=39\) km down, \(3\times7=21\) km up; \(39-21=18\) km