A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream
Answers
Step-by-step explanation:
Let the speed of stream be x km/hr
speed of boat in upstream = (18 - x)
speed of boad in downstream = (18 + X)
ATQ,
Time = Distance/Speed
(Upstream time - downstream time) = Time difference
24/(18-x) - 24/(18+x) = 1
24 (18+x -18 + x ) = X² + 324
24(2x) = X² + 324
X² - 48x + 324 = 0
x² - 54x + 6x + 324 = 0
(X - 6) (x + 54) = 0
X = 6. ; X ≠ -54
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