A motorboat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km upstream that to return downstream to the same spot. Find the speed of the stream.
Time = Distance/speed
Given, motorboat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km upstream that to return downstream to the same spot.
Let the speed of stream be ‘a’ km/hr.
Relative speed of boat going upstream = 18 – a km/hr
Relative speed of boat going downstream = 18 + a km/hr
⇒ 24(18 + a – 18 + a) = -a2 + 324
⇒ a2 + 48a – 324 = 0
⇒ a2 + 54a - 6a – 324 = 0
⇒ a(a + 54) – 6(a + 54) = 0
⇒ (a – 6)(a + 54) = 0
⇒ a = 6 km/hr