College Algebra Math Problem
Bradley
wide. A factory is six miles downstream on the other side of the river. It
costs $18 per foot to run power lines overland and $24 per foot to run them
underwater. The total cost of the project is $616,877.27. Find the length x
as labeled in the figure.
(The answer in the back of the math book is .26mi or 1mi).
I was told to solve this problem I should use pythagorean theorem. And I
know it can be solved that way. But could it also be solved with the
following equation?
24x + 18(31680 - x) = 616,877.27
The 31680 being 6 miles in actual feet (5280*6). I have actually solved the
above equation and come up with an answer of x = 1.472136048. Which is not
the correct answer for this problem but it has to be relevant somehow to it
since I got exactly one solution. Can somebody please help me understand
this? Thank You.
P.S. The pythagorean equation I am using is:
18*sqrt(x^2 + 2640^2) + 24(31680 - x) = 616,877.27
Is this equation correct? This problem blows my mind. Thanks for all the
help.
Jim Spriggs
>
> .... Find the length x
> as labeled in the figure.
What figure?
mensa...@aol.com
Bradley wrote:
> Power Line - A power station is on one side of a river
> that is 1/2 mile wide. A factory is six miles downstream
> on the other side of the river. It costs $18 per foot to
> run power lines overland and $24 per foot to run them
> underwater. The total cost of the project is $616,877.27.
> Find the length x as labeled in the figure.
I'll assume the figure is something like
PS
|\
0.5 | \h
| \
------------------F
| x |
| 6 |
> (The answer in the back of the math book is .26mi or 1mi).
Actually, 0.26 would be off by 10 feet. Should be 0.261831
but the book answer is correct to 2 decimal places, so we'll
let that slide.
>
> I was told to solve this problem I should use pythagorean
> theorem. And I know it can be solved that way. But could
> it also be solved with the following equation?
>
> 24x + 18(31680 - x) = 616,877.27
No. Your overland part is correct, but x does not cross
the river, line h does. Your formula should be
24h + 18(31680 - x) = 616,877.27
>
> The 31680 being 6 miles in actual feet (5280*6). I have
> actually solved the above equation and come up with an
> answer of x = 1.472136048.
Do you see why the answer is wrong?
> Which is not the correct answer
> for this problem but it has to be relevant somehow to it
> since I got exactly one solution.
No, it doesn't have to be relevant. You priced only 6 miles
of cable (incorrectly by applying two different costs). 6 miles
of cable will not reach the power station regardless of how
you route it.
> Can somebody please help me understand this? Thank You.
>
> P.S. The pythagorean equation I am using is:
>
> 18*sqrt(x^2 + 2640^2) + 24(31680 - x) = 616,877.27
>
> Is this equation correct?
No, but I'll give you the benefit of doubt and assume you
just typed it in wrong in your post. You have the costs
reversed, should be:
24*sqrt(x^2 + 2640^2) + 18(31680 - x) = 616,877.27
> This problem blows my mind.
In case you're wondering why there are two answers, 0.26mi
and 1mi. it's because the cost is non the minimum possible.
If line h was 0.567mi the cost would have been $612,148.70
so there is a higher cost point on either side of this.