Question 285655
Jen’s boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water. 
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You will need to apply the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
However, for this problem we are going to solve for t:
d = rt
d/r = t
t = d/r
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Let x = speed of boat in still water
then
x+3 = speed going downstream
x-3 = speed going upstream
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"time going upstream" + "time going downstream" = 8
45/(x+3) + 45/(x-3) = 8
multiplying both sides by (x+3)(x-3):
45(x-3) + 45(x+3) = 8(x+3)(x-3)
45x - 135 + 45x + 135 = 8(x^2-9)
90x = 8x^2-72
0 = 8x^2-90x-72
0 = 4x^2-45x-36
Factoring the right:
0 = (4x+3)(x-12)
x = {-3/4 , 12}
Well we can toss out the negative answer leaving:
x = 12 mph  (speed in still water)