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Question
A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat in still water and the speed of the stream.
Solution
Let the speed of the boat in still water be x km/hr
and the speed of the stream be y km/hr.
Speed of the boat upstream = (x - y)km/hr.
Speed of the boat downstream = (x + y)km/hr
Time required to go 18 km upstream = 3 hours
⇒ `(18)/(x - y)` = 3
⇒ `(6)/(x - y)` = 1
⇒ x - y = 6 ....(i)
Time required to go 24 km downstream = 2 hours
⇒`(24)/(x + y)` = 2
⇒ `(12)/(x + y)` = 1
⇒ x + y = 12 ....(ii)
Adding eqns. (i) and (ii), we get
2x = 18
⇒ x = 9
⇒ 9 - y = 6
⇒ y = 3
Thus, the speed of the boat in still water is 9 km/hr and the speed of the stream is 3km/hr.
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