# Help with this problem!

1. Jul 17, 2010

### Slimjimjohnso

A steel pipe is being carried horizontally down a hallway that is 9ft wide. At the end of the hallway there is a right turn into a hallway that is 6ft wide. What is the length of the longest pipe that can be carried horizontally around the corner? (Hint: minimize the line)

I have looked at this problem and tried many ways to solve it. I cannot think of a way to relate my information to make a derivable function.

I did make a bunch of triangles and using geometry I'm pretty sure the answer is 21ft but man if I can't do this with calculus. Help!

2. Jul 17, 2010

### xcvxcvvc

21ft? That's longer than both hallway's are wide put together.

3. Jul 17, 2010

### Slimjimjohnso

Imagine an L shaped hallway. The short part of the L is 9ft the long part is 6ft. If you drag one side along the 9ft part around the corner into the 6ft part why couldn't it be 21ft?

I would show the picture I have drawn but I am on my phone at work and don't have a way to post it here.

4. Jul 17, 2010

### Slimjimjohnso

5. Jul 17, 2010

### xcvxcvvc

The problem states that the steel pipe begins by being carried horizontally down a hallway that is 9 ft wide... sorry but this is just a horrible wording of the question if that diagram was the setup in mind.

6. Jul 17, 2010

### Slimjimjohnso

The problem and picture is directly off of my homework.

I added the lines in between the L shaped hallway. But the line is the hypotenuse of a bigger triangle. The only thing I can think to relate the problem to calculus is through some sort of trig identities.

7. Jul 17, 2010

### vela

Staff Emeritus
Break the length of the pipe into two pieces, x1 and x2, where x1 is the portion that's in the 9' hallway and x2 is the portion in the 6' hallway. Relate these lengths to the angle θ and the width of the respective hallway. You'll get an expression for the total length of the pipe L=x1+x2 as a function of θ. That's the function you want to minimize.

8. Jul 18, 2010

### Slimjimjohnso

Thank you very much for your help.

I ended up with

I took cos(theta)=9/a and sin(theta)=6/b
To get my function

L(theta)=9sec(theta)+6csc(theta)