# Word problems: polynomial equations? its worth 10 points! please take some time to help me?

1. The length of a rectangular box is one inch greater than its width. The height is three times

the length. The diagonal of the box exceeds the height by one inch. Find the volume of the

box.

2. A trip between two cities 175 miles apart take 1.5 hours less by train than by bus. The average

speed of the bus is 15 miles per hours less than the train. Find the average speeds of the train

and the bus.

3. The length of a room exceeds the width by 5 feet, and the height is 3 feet less than the width.

The area of the four walls exceeds the sum of the areas of the floor and the ceiling by 240

square feet. Find the dimensions of the room.

4. A rectangular piece of cardboard is 15 inches longer than it is wide. If 5-inch squares are cut

from each corner, and the remaining piece folded up to form a box, the volume of the box is

1250 cubic inches. Find the dimensions of the piece of cardboard.

5. A party of students rented a motor boat, B, and shared to cost equally. If the number of

students had been 5 less, they could have used a smaller boat costing only half as much as B

and the expense to each would have been 50 cents less. If there had been 10 more students in

the party, they would have required a larger boat costing 20% more than B, but the expense

to each would have been 30 cents less. How many students were in the party?

6. It will take a boy 15 days longer than a man to paint a certain house, but if 3 boys and 2 men

work together the whole job can be completed in 3 1/8 days. How long does it take a boy to

paint the house alone?

7. A monument consists of two cubical blocks of granite, the smaller resting on the larger. The

total height of the monument is 5 feet, and the area of the exposed surface is 61 square feet.

please do as many as you can. i m soo confused i don't get it.

and explain!

Relevance

se help?

LeRoy, a starting player for a major college basketball team,

made only 40% of his free throws last season.

During the summer, he worked on developing a softer shot in hopes of improving his free throw

accuracy. In the first eight games of this season, LeRoy made 23 free throws in 40 attempts.

4. Based on this data, is there convincing evidence that LeRoy’s work over the summer resulted in a

higher proportion of free throw successes this season? Let the significance level = 0.05.

I am having trouble doing this problem... Can someone help? Show work plz?

Word problems: polynomial equations? its worth 10 points! please take some time to help me?

1. The length of a rectangular box is one inch greater than its width.

The height is three times the length.

The diagonal of the box exceeds the height by one inch.

Find the volume of the box.

Not sure of which diagonal, because there are 2 or 3 different diagonals, top view, front view, or side view, plus 2 others.

Consider l=x, w=x-1,; h=3x, and

diagnal d: =h^2 +l^2 = (3x)^2 +x^2 =(3x +1)^2

9x^2 +x^2= 9x^2 +6x +1

x^2 -6x +(3^2) =1 +3^2 (this completing the square)

(x-3)^2 =10

sqrt each side

x-3= sqrt 10

x= sqrt10 -3;

x=l=6.1623 ; w=5.1623; h=18.4868; V= 588.0918 cub inches

2. A trip between two cities 175 miles apart take 1.5 hours less by train than by bus. The average

speed of the bus is 15 miles per hours less than the train. Find the average speeds of the train

and the bus.

175 =x(t) for train

175= (x-15)(t+1.5) for bus

Since 175 =xt, then x= 175/t; sun into 2nd equation

175= (175/t -15)(t +3/2)

175 = 175 + 262.5/t -15t -22.5

0= 262.5-15t^2-22.5t

multiply all by -2

0= 30t^2 +45t-525

0= 2t^2 +3t -35

(2t-7)(t+5)

2t=7

t=7/2=3.5 for train

Not always true, but in this case, total time=5 for bus

So 175/3.5 = speed of train =50 mph

175/5- speed of bus= 35 mph

3. The length of a room exceeds the width by 5 feet,

and the height is 3 feet less than the width.

The area of the four walls

exceeds the sum of the areas of the floor and the ceiling by 240

square feet. Find the dimensions of the room.

w+5=L; w=L-5; h=w-3>>w=h+3

L-5=h+3; L=h+8; h=L-8

2(Lh) +2(l-5)h = 2(L-5)(L) +240

4Lh-10h =2L^2-10L +240

h(4L-10) =2L^2-10L +240

(L-8)(4L-10) =2L^2-10L +240

4L^2 -42L+ 80 =2L^2-10L +240

2L^2-32L -160 =0

L^2-16L -80 =0

(L-20)(L+4)

L-20=0

L=20

H=12

W=15

4. A rectangular piece of cardboard is 15 inches longer than it is wide. If 5-inch squares are cut

from each corner, and the remaining piece folded up to form a box, the volume of the box is

1250 cubic inches. Find the dimensions of the piece of cardboard.

35L X 20 W

Really need to draw this to see it clearly;

Let x =l and x-15 = w, and because of the 5 -inch cuts, the height =5

After cutting we loose 10 inches on length, thus x-10

We loose 10 inches on width, so x-15-10 or x-25

(x-10)(x-25)(5) =1250

(x-10)(x-25) =250

x^2 -35x +250 -250=0

x^2 -35x=0

x^2=35x

x=35=L

35 -15 =20 =W

5. A party of students rented a motor boat, B, and shared to cost equally.

If the number of students had been 5 less, they could have used a smaller boat costing only half as much as B

and the expense to each would have been 50 cents less.

If there had been 10 more students in

the party, they would have required a larger boat costing 20% more than B, but the expense

to each would have been 30 cents less. How many students were in the party?

No quite sure of the question; is any information missing?

6. It will take a boy 15 days longer than a man to paint a certain house, but if 3 boys and 2 men

work together the whole job can be completed in 3 1/8 days. How long does it take a boy to

paint the house alone?

2/x +3/(x+15) =25/8

(2(x+15) +3(x))/x(x+15) =25/8

(2x +30 +3x)/(x^2 +15x) =25/8

8(5x +30) =25(x^2 +15X)

40X +240 =25X^2 + 375x

25X^2 +335X =240

x^2 +13.4x = 9.6

x^2 +13.4x +(6.7)^2 =9.6 +(6.7)^2

(x+6.7)^2 = 54.49

(x+6.7) = 7.3817

x= 7.3817 -6.7=0.68173 = how fast 1 man can do job

x+15 =15.68173 = how long does it take a boy to

paint the house alone?

7. A monument consists of two cubical blocks of granite, the smaller resting on the larger. The

total height of the monument is 5 feet, and the area of the exposed surface is 61 square feet.

No quite sure of the question; is any information missing?

• 1. assume the width(W) is a, so length(L) = a +1, height(H) is 3(a + 1), the diagonal line(D) is3(a + 1)+1

use the relation between all these measurements: W^2 + L^2 + H^2 = D^2. And then you can solve for a, and the volume.

2. Let Tt be the time for the train, and Tb be the time for bus. From the context above, you can easily figure out the relation between both: Tt = Tb - 1.5. The speed for bus is Vb and for train is Vt, and their relation is Vt = Vb + 15. Therefore, 175/Vt = 175/Vb -15, and you can replace Vt with the Vb - 1.5 to solve for speed of the train and the bus.

• it ends up being 0=20 which is NO SOLUTION. both the x and y values cancel out (that's where the 0 came from) SO... if you are graphing a system of equations than they are parallel lines because they have the same slope