A power station is on one side of a river that is 3/4 mile wide, and a factory is 8 miles downstream on the other side of the river. It costs $24 per foot to run power lines over land and $30 per foot to run them under water.(1 mile = 5280 feet)

Question

Write the total cost C to run power lines in term of x?

P.S. the diagram that went along with this had a ______ that represented 8-x and a slanted line that represented x "/"

Steve · Answer

Consider the point on shore that is closest to the station.

I can't tell from your explanation, but I will say that x is the distance from there to where the line comes ashore. That means 8-x is the rest of the way to the factory.

So, using the Pythagorean Theorem, the distance from the power station to where the line comes ashore is

d^2 = x^2 + (3/4)^2

So, the cost is

30d + 24(8-x)
= 30√(.75^2+x^2) + 24(8-x)

If I got x and 8-x mixed up, I'm sure you can make the fix...