Math Is Fun Forum

Slowlrnr

Member

Registered: 2010-01-26

Posts: 14

Word problems assistance

How would you set up the formula?

A farmer has 3000 feet of fencing and wishes to enclose a rectangular area. What is the maximum area he can enclose?
-----------------------
Beth can walk six miles in the same time she can bike 32 miles.If her biking rate is one more than five times her walking rate, how fast does she walk?

Is it 6/x= 32/5x+1  ? if so , then x = 1/2?  I then  used f(1/2) = 5x+1 and got 3.5 . Is this correct and what does this 3.5 relate to ?  I am confused..

Thank you for your time.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Word problems assistance

Hi Slowlrnr;

The maximum rectangle for enclosing area for a given perimeter is a square. Here is how you prove that.

You can use calculus:

2L + 2W = 3000

A = L * W

Solve for L:

L = (1500 - W)

A = (1500 - W) W = 1500W - W^2

Set that equal to 0.

1500 - 2W = 0

W = 750 so L = 750 , A = 750^2 = 562500 square ft. This is the maximum area for 3000 ft of fence.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Word problems assistance

Hi Slowlrnr;

I don't think the second answer is correct.

I solve it like this:

B * t = 32
W * t = 6
B =5W + 1

Where B is the Bike rate, W is walk rate and t is the time.

Solve them simultaneously by substittutions:

( 5W + 1) t = 32

W * t =6

Now substitue t = 6 / W

( 5 W + 1) ( 6 / W) = 32

30  + 6 / W = 32

6 / W = 2

W = 3.

So

B = 16 , W = 3, t = 2

For what you did, your equation is correct you just solved it incorrectly.

Cross multiply:

x = 3 , same as above.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Slowlrnr

Member

Registered: 2010-01-26

Posts: 14

Re: Word problems assistance

So what does the 3 represent in the walking equation?  I see my error wih the multiplication but the question was asking for "how fast does she walk?".

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Word problems assistance

that's the Speed!
in miles per unit time!

---

If two or more thoughts intersect, there has to be a point!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Word problems assistance

Hi;

Rate that was used twice in the question means speed or velocity. My solutions are based on d = rate * time  or d = velocity  * time . Solving for B and W is solving for rate or velocity.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.