Solve the quadratic and polynomial equations.

[helphelphelphelp]

Two questions:

Solve by Completing the square.
A road around a 6m by 9m garden is the same width on all four sides. If the area of the road is the same as the area of the garden, how wide is the road?
What I have as the starting equation: (9 + 2X)(6 + 2X) - (54) = 54 Problem: After solving, I don't understand why I need to complete the square.
*I think you should do it yourself. My work might not be 100% right.*

Solve using the quadratic formula. With exact answers.
Wendy and Peter ride their bikes from home to the country, a distance of 120km. Peter rides 6 km/h faster than Wendy, and takes an hour less for the trip. How fast does each person ride?
Problem: Don't know how to write the equation
Not a problem: I know how to do the quadratic formula

 

[Denis]

A road around a 6m by 9m garden is the same width on all four sides. If the area of the road is the same as the area of the garden, how wide is the road?
What I have as the starting equation: (9 + 2X)(6 + 2X) - (54) = 54 Problem: After solving, I don't understand why I need to complete the square.

That's correct; you should state: let x = width of road
I guess you need "to complete the square" because the teacher said so!

Wendy and Peter ride their bikes from home to the country, a distance of 120km. Peter rides 6 km/h faster than Wendy, and takes an hour less for the trip. How fast does each person ride?
Problem: Don't know how to write the equation

Use formula s = d/t : speed = distance/time

Let p = Peter's speed; then Wendy's speed = p - 6
Let h = Peter's time; then Wendy's time = h + 1
All yours!

 

[DrMike]

Two questions:

Solve by Completing the square.
A road around a 6m by 9m garden is the same width on all four sides. If the area of the road is the same as the area of the garden, how wide is the road?
What I have as the starting equation: (9 + 2X)(6 + 2X) - (54) = 54 Problem: After solving, I don't understand why I need to complete the square.

Completing the square is a method of solving. It's something you do before you solve, not after. You may know how to solve it via other methods, but this question wants you to use a specific method for solving it.

Basically, if you have ax[sup:15mbf1nm]2[/sup:15mbf1nm]+bx+c, you 'complete the square' by writing this as \(\displaystyle a(x^2+\frac{b}{a}x)+c\), then note that \(\displaystyle x^2+\frac{b}{a}x=(x+\frac{b}{2a})^2-\frac{b^2}{4a^2}\)

Solve using the quadratic formula. With exact answers.
Wendy and Peter ride their bikes from home to the country, a distance of 120km. Peter rides 6 km/h faster than Wendy, and takes an hour less for the trip. How fast does each person ride?
Problem: Don't know how to write the equation
Not a problem: I know how to do the quadratic formula

Let W be Wendy's speed, and P be Pete's speed. Can you write an equation for the following?

Peter rides 6 km/h faster than Wendy

Or what about a formula for

How long does Pete take to ride 120km?

Or for

How long does Wendy take to ride 120km?

Then get an equation for

Peter ... takes an hour less for the trip.

Now you have two equations. Eliminate one of the variables, and solve. Do each step carefully, and check your answers at the end.

 

[helphelphelphelp]

Can someone run me through Wendy and Peter again?
I don't know why I have trouble doing this one question. Here's the formula i came up with:
(x+6)(y-1)= 120

now what?

 

[DrMike]

Can someone run me through Wendy and Peter again?
I don't know why I have trouble doing this one question. Here's the formula i came up with:
(x+6)(y-1)= 120

now what?

What are your x and y?

If w is Wendy's speed, and p is Peter's, I get

Wendy takes 120/w hours, Peter takes 120/p.

Peter takes an hour less, so 120/p = 120/w - 1

Multiplying by p and w, we get

120 w = 120 p - pw.

Then, remember that p = 6+w......

I'll stop here for now...

 

[stapel]

Solve using the quadratic formula. With exact answers.
Wendy and Peter ride their bikes from home to the country, a distance of 120km. Peter rides 6 km/h faster than Wendy, and takes an hour less for the trip. How fast does each person ride?
Problem: Don't know how to write the equation

To learn the basic method for setting up and solving this sort of exercise, try here. Once you are familiar with the terms and techniques....

i) Since Peter's speed is defined in terms of Wendy's, pick a variable for Wendy's speed.

ii) In terms of the variable in (i), create an expression for Peter's speed.

iii) Noting that "d = rt" (so t = d/r), and that d = 120, create an expression, in terms of the variable in (i), for Wendy's travel time.

iv) Using the same reasoning as in (iii) and the expression in (ii), create an expression for Peter's travel time.

v) Translate the relationship "(Peter's time) is (Wendy's time) less (one hour)" into an equation.

vi) Multiply through to clear the denominators.

vii) Solve the resulting quadratic equation.

If you get stuck, please reply showing how far you have gotten. Thank you!

 

[helphelphelphelp]

k here goes:

let x be wendy and x+6 be peter.

x(120/x) = (x+6)(120/x-1)

right? because x(120/x) is wendy and (x+6)(120/x-1) is essentially all the info i have on peter