Motorboat whose speed is 18 kilometre per hour in still water takes 1 hour to go 24 km upstream then to return downstream to same spot find the speed of the stream
Answers
Step-by-step explanation:
Speed of MotorBoat = 18 km/hr
Let say speed of stream = S km/Hr
Down Stream speed = 18 + S km/Hr
Upstream Speed = 18 - S km/Hr
Distance each side = 24 km
Time taken for upstream = 24/(18 -S) hr
Time Taken for Downstream = 24/(18 + S) hr
Time taken for upstream is 1 hr more than downstream
24/(18-S) - 24/(18+S) = 1
Multiplying both sides by (18-S)(18+S)
=> 24 (18 + S) - 24(18-S) = (18-S)(18+S)
=> 24 ( 2S) = 324 - S²
=> S² + 48S - 324 = 0
=> S² + 54S - 6S - 324 = 0
=> S(S+54) - 6(S+54) = 0
=> (S-6) (S +54) = 0
=> S = 6 ( S can not be - ve)
Speed of stream = 6 km/hr
Let the speed of the stream be x km\hr.
The speed of the boat upstream = (18 - x) km/hr
The speed of the boat downstream = (18 + x) km/hr
Distance = 24 km
As given in the question,
Time for upstream = 1 + Time for downstream
24/(18 - x) = 1 + 24/(18 + x)
24/(18 - x) - 24/(18 + x) = 1
x2 + 48x - 324 = 0
(x + 54)(x - 6) = 0
x ≠ - 54 as speed cannot be negative.
x = 6
The speed of the stream = 6 km/hr