Answer:
4kph
Step-by-step explanation:
Let x be the speed of the boat
Speed of the river = 2 kph
Total time spent = 8 hours
Distance = 12 km
Speed of the boat upstream ( against the river current) = x - 2
Speed of the boat downstream ( along with the current ) = x +2
The formula for t = d/s
Where
d is distance
s is speed
Therefore the working equation would be
time for downstream + time for upstream = 8 hours
[tex]\frac{12}{x+2} + \frac{12}{x-2} = 8[/tex]
Multiplying both sides (x+2)(x-2) by for the purpose of eliminating fractions
[tex]\frac{12(x+2)(x-2)}{x+2} + \frac{12(x+2)(x-2)}{x-2} = 8(x+2)(x-2)\\[/tex]
Cancel same terms
12(x-2) + 12(x+2) = 8(x+2)(x-2)
Solving further
[tex]12x-24+12x+24 = 8x^2 - 32[/tex]
[tex]24 x = 8x^2 - 32\\8x^2 -24x- 32 = 0\\x^2 - 3x -4 = 0\\\\\text {Factoring}\\(x-4)(x+1) = 0[/tex]
Finding the roots
x-4 = 0
x = 4
x+1 = 0
x = -1
Disregarding the negative value of x ,
The answer therefore is 4 kph for the speed of the boat in still water
Checking
[tex]\frac{12}{4+2} + \frac{12}{4-2} = 8\\2+6 =8\\8 =8[/tex]
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