SOLUTION: I have a word problem but I am stuck. the current in a stream moves at a speed of 3mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hours. What is

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Question 173348This question is from textbook
: I have a word problem but I am stuck.
the current in a stream moves at a speed of 3mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hours. What is the speed of the boat in still water?
45/r-3 + 45/r+3 = 8
45(r+3) + 45(r-3)= 8(r+3)(r-3)
90r = 8r^2 - 72
and I'm stuck This question is from textbook

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're off to a great start. I'll start where you left off.



90r+=+8r%5E2+-+72 Start with the given equation


0+=+8r%5E2+-+72-90r Subtract 90r from both sides.


+0=+8r%5E2-90r+-+72 Rearrange the terms.


Notice we have a quadratic equation in the form of ar%5E2%2Bbr%2Bc where a=8, b=-90, and c=-72


Let's use the quadratic formula to solve for r


r+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


r+=+%28-%28-90%29+%2B-+sqrt%28+%28-90%29%5E2-4%288%29%28-72%29+%29%29%2F%282%288%29%29 Plug in a=8, b=-90, and c=-72


r+=+%2890+%2B-+sqrt%28+%28-90%29%5E2-4%288%29%28-72%29+%29%29%2F%282%288%29%29 Negate -90 to get 90.


r+=+%2890+%2B-+sqrt%28+8100-4%288%29%28-72%29+%29%29%2F%282%288%29%29 Square -90 to get 8100.


r+=+%2890+%2B-+sqrt%28+8100--2304+%29%29%2F%282%288%29%29 Multiply 4%288%29%28-72%29 to get -2304


r+=+%2890+%2B-+sqrt%28+8100%2B2304+%29%29%2F%282%288%29%29 Rewrite sqrt%288100--2304%29 as sqrt%288100%2B2304%29


r+=+%2890+%2B-+sqrt%28+10404+%29%29%2F%282%288%29%29 Add 8100 to 2304 to get 10404


r+=+%2890+%2B-+sqrt%28+10404+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


r+=+%2890+%2B-+102%29%2F%2816%29 Take the square root of 10404 to get 102.


r+=+%2890+%2B+102%29%2F%2816%29 or r+=+%2890+-+102%29%2F%2816%29 Break up the expression.


r+=+%28192%29%2F%2816%29 or r+=++%28-12%29%2F%2816%29 Combine like terms.


r+=+12 or r+=+-3%2F4 Simplify.


So the possible answers are r+=+12 or r+=+-3%2F4

However, a negative speed doesn't make sense. So we'll discard the possible solution r+=+-3%2F4



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Answer:


So the solution is r+=+12 which means that the speed of the boat in still water is 12 mph.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the current in a stream moves at a speed of 3mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hours. What is the speed of the boat in still water?
------------------
Upstream DATA:
distance 45 miles; rate = b-3 mph ; time = 45/(b-3)
------------------------
Downstream DATA:
distance = 45 miles ; rate = b+3 mph ; time = 45/(b+3)
-------------------------
time + time = 8 hrs.
45/(b-3) + 45/(b+3) = 8
45(b+3) + 45(b-3) = 8(b^2-9)
90b = 8b^2-72
8b^2-90b-72 = 0
Use the quadratic formula whenever you cannot see the factors:
b = [90 +- sqrt(8100 - 4*8*-72)]/16
b = [90 +- sqrt(10404)]/16
b = [90 +-102]/16
Positive solution:
b = 192/16 = 12 mph (speed of the boat in still water)
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Cheers,
Stan H.