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

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) (Show Source): You can put this solution on YOUR website!
You're off to a great start. I'll start where you left off.

Start with the given equation

Subtract 90r from both sides.

Rearrange the terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for r

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, a negative speed doesn't make sense. So we'll discard the possible solution

==========================================================

Answer:

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

Answer by stanbon(75887) (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)
========================================================
Cheers,
Stan H.
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