word problem help?

Question

1)the perimeter of a rectangle is 44 inches and its area is 112 square inches. find the length and the width of the rectangle.

2)it takes terry 2 hours longer to do a certain job than it takes tom. they work together for 3 hours: then tom left and terry finished the job in 1 hour. how long would it take each of them to do the job alone.

Answer 1

1) Let w = the width, and 22-w = the length. (l+w=P/2) Put those into the area formula, so w(22-w) = 112. You get 22w - w^2 = 112, sort that around and get w^2 - 22w + 112 = 0. You'll have to use the quadratic formula to solve for w, because it won't factor rationally.

Answer 2

perimeter of rectangle = 2x+2y area = xy = 112 x = 112/y

2x+2y = 44 (now divide both sides by 2) x+y = 22

substitute 112/y for x and you get 112/y +y = 22

multiply everything by y you get 112 + y^2 = 22y
y^2 - 22y +112 = 0 (y-14) (y-8)
rectangle = 8 X 14 perimeter = 8+8+14+14 = 44 area = 8(14) = 112

tom does the job in x hours and terry in x+2 hours

in one hour tom does 1/x of the job and terry 1/(x+2)

so in 3 hours tom does 3/x and terry does 3/(x+2) and then terry does 1/(x+2) and the job is done

3/x + 3/(x+2) + 1(x+2) = 1 (the whole job is done)

3/x +4/(x+2) = 1
multipoly both sides by x(x+2)
3 (x+2) + 4 (x) = x (x+2)
3x+6 +4x = x^2 +2x
7x + 6 = x^2 +2x
x^2 - 5x -6 = 0 (x-6) (x+1) = 0
tom gets the job done in 6 hrs, and Terry in 6+2 or 8 hours

put it back in the problem Tom works 3 hrs = 1/2 the job
Terry works 4 hrs and does half the job : he would finish it all in 8 hrs by himself

Answer 3

Let the length be l inches, and the width be w inches.
Perimeter = 2*length + 2*width
44 = 2l + 2w
44 = 2(l + w)
22 = l + w
l = 22 - w
Area = length * width
112 = l * w
112 = (22 - w) * w
112 = 22w - w^2
w^2 - 22w + 112 = 0
(w - 8)(w - 14) = 0
w - 8 = 0
w = 8
l = 22 - w = 22 - 8 = 14
w - 14 = 0
w = 14
l = 22 - w = 22 - 14 = 8
Hence, the dimensions of the rectangle are 14 inches by 8 inches.



Next Answer =
let's say it takes terry r hours to finish the job alone.
then it takes tom r - 2 hours to finish the job along.
1/r of the job is done by terry in 1 hour
1/(r-2) of the job is done by terry in 1 hour
so
amount of job done by tom and terry + amount of job done by terry alone = 1
(1/r + 1/(r-2))*3 + 1/r = 1
3/r + 3/(r-2) + 1/r = 1
4/r + 3/(r-2) = 1 multiply everything by r(r-2)
4(r-2) + 3r = r(r-2)
4r - 8 + 3r = r^2 - 2r
r^2 - 9r + 8 = 0
(r-1)(r-8) = 0
r = 1 or r = 8
since tom takes r - 2 hours to do the job alone
tom takes 8 - 2 = 6 hours
and terry takes 8 hours

Answer 4

1) 14in x 8in rectangle 14+14+8+8=44
14x8=112
This is for sure!
2) terry takes 6hrs while tom takes 4
Im guessing though!!
But considering that together it took them 3 hrs then terry did 1 more hr on top that puts him at 4

Answer 5

1)
2(L+W)=44
L+W=22 => L=22-W
L*W=112
(22-W)*W=112
W^2 - 22W + 112 = 0
(W-14)(W-8)=0
W=8 or 14
L=8 or 14

The length and the width are 8 feet and 14 feet.

2)
Assume it takes Terry x hours to do the job. Therefore, it takes Tom (x-2) hours to finished it.
In an hour, Terry finishes 1/x of the job and Tom finishes 1/(x-2) of the job.

After three hours, they finished: 3* ( 1/x + 1/(x-2) ) = (6x-6)/(x(x-2)) of the job

After that, Terry finished it in an hour

(6x-6)/(x(x-2)) + 1/x = 1
7x-8 = x^2 - 2x

x^2 - 9x + 8 = 0

(x-1)(x-8)=0
x=1, 8

Terry can finish the job alone in 8 hours, and Tom can finish it in 6 hours.

Answer 6

1) P=2x +2y
x is length y is width
A=xy -->112/x=y
Substitue that y into the first equation....
44=2x +2(112/x)
22=x +112/x keep solving for x
when u have the value of x u can insert it in 112/x= y
find y then u have both length and width.

2) cant help u its too late for me to think that hard :)

Answer 7

1) Perimeter = 44
Semi perimeter = 44/2 = 22
Let the Length be = x
Width = 22 - x
Area = x(22-x) = 22x - x² = 112
x² - 22x + 112 = 0
Solve 'x' and then find lngth