Answer: the speed of the stream is 6 km/h
Step-by-step explanation:
Let x represent the speed of the stream.
The speed of the motor boat in still water is 18km/h. The boat takes 1 hour more to go 24 km upstream than downstream to the same spot. This means that while going upstream, the boat moved against the direction of the stream. The total speed of the boat would be
(18 - x) and while going downstream, the boat moved in the direction of the stream. The total speed of the boat would be
(18 + x).
Time = distance/speed
The time that it took the boat to go upstream is
24/(18 - x)
Time spent upstream = time spent downstream + 1
The time that it took the boat to go downstream is
24/(18 + x) + 1
Therefore,
24/(18 - x) = 24/(18 + x) + 1
Multiplying through by 18 - x and 18 + x, it becomes
24(18 + x) = 24(18 - x) + (18 + x)(18 - x)
432 + 24x = 432 - 24x + 324 - 18x + 18x - x²
x² + 432 - 432 + 24x + 24x - 324 = 0
x² + 48x - 324 = 0
x² + 54x - 6x - 324 = 0
x( x + 54) - 6(x + 54) = 0
x - 6 = 0 or x + 54 = 0
x = 6 or x = - 54
Since the speed cannot be negative, then x = 6km/h
