Question 212720
Boat Speed. The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?
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Applying the distance formula:
d = rt)
Solving for t:
t = d/r
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Let r = speed of boat in still water
then
"time going upstream" + "time going downstream" = 8
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45/(r-3) + 45/(r+3) = 8
Now, multiplying both sides by (r-3)(r+3):
45(r+3) + 45(r-3) = 8(r-3)(r+3)
Expanding:
45r+135 + 45r-135 = 8(r^2-9)
45r+45r = 8r^2-72
90r = 8r^2-72
0 = 8r^2-90r-72  (Exactly what you had)
Solving for r using the quadratic formula yields:
r = {12, -0.75}
We can toss out the negative answer leaving:
r = 12 mph
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Details of quadratic to follow:
*[invoke quadratic "r", 8, -90, -72 ]