auxiarc

First, find out how long it would take them to read the same book. You can do this by cross multiplying.

Because it asks for the answer in minutes, change the 1 hour to 60 minutes.

Xavier

100 pgs / 60 mins = 225 pgs / x mins

100x = 255(60)                                        multiply

100x = 15300                                           divide 100 on both sides

x = 153

From this information, we can gather that it will take Xavier 153 minutes to read the book.

Now, calculate how long it'll take Max to read the book.

Max

50 pgs / 60 mins = 225 pgs / x mins 

50x = 255(60)                                          multiply

50x = 15300                                             divide 50 on both sides

x = 308

It will take Max 308 minutes to read the book.

The question asks how many more minutes than Xavier does it take for Max to finish reading the book.

Subtract the minutes it would take Xavier to read the book from the amount of minutes it would take Max to read the book. 

308 - 153 = 155

It takes 155 more minutes than Xavier for Max to finish the book.

Given that the longer leg of the right triangle is one foot less than twice the shorter leg, we can set up an equation that will help find the length of the shorter and longer leg.

a = x ft

b = 2x - 1 ft

c = 17 ft

Using the pythagorean theorem, a² + b² = c², you can find the length of both the shorter and longer leg.

a² + b² = c²

x² + (2x -1)² = 17²

x² + 2x² + 1 = 289

               -1       -1

3x² / 3 = 288 / 3

x² = 96

sqrt(x²) = sqrt(96)

x = 9.8

The length of the shorter leg is 9.8 ft. 

To find the length of the longer leg, substitute 9.8 for x in 2x - 1.

2(9.8) - 1 =

19.6 - 1 

18.6

The length of the longer leg is 18.6 ft.

To find the area of a triangle, multiply the base by the height, and then divide by 2.

area = ( 9.8 x 18.6 ) / 2 

area = 182.28 / 2

area = 91.12 ft

The area of the triangle is 91.12 ft.

List the factors of 216.

 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Since his ID code is only three-digits, we can eliminate the numbers above 9, which leaves us to:

 - 1, 2, 3, 4, 6, 8, 9

Use these numbers to determine what 3 numbers add to equal 19 and multiply to equal 216.

The numbers in Angel's ID code include: 4, 6, and 9.

List the possible three-digit outcomes of 4, 6, 9 (hint - since there are three digits, there are 6 outcomes):

4-6-9

4-9-6

9-4-6

9-6-4

6-9-4

6-4-9

The last bit of information also tells us that the integer code is as large as possible. Picking from the list of possible three-digit outcomes, ask yourself, which is the largest possible?
 

Angelo's ID code is 9-6-4.

If you have any questions, don't be afraid to ask! I hope I explained well enough. 

:)

List the factors of 60.

 - 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Then determine what two numbers subtract to equal 7 and multipy to equal 60.

a = 12

b = 5

To find sqrt(a^2 + b^2), substitute the values of a and b like so:

sqrt((12)^2 + (5)^2) =

sqrt(144 + 25) = 

sqrt(169) = 13

(x + y)/2 = 5

sqrt(xy) = 3

sqrt(xy)²=3²                     Square both sides to eliminate the square root on the left side.

xy = 9

(xy)/x = 9/x                       Divide x on both sides.

y = 9/x

Now that you know y, you can solve for x by using the first equation given.

(x + y)/2 = 5

(x+(9/x))/2 = 5                   Substitute 9/x into the value of y.

(x+(9/x))/ 2 ⋅ 2 = 5 ⋅ 2        Multiply 2 on both sides to get rid of the denominator on the left side.

x+(9/x) = 10

x+(9/x) - x = 10 - x            Subtract x on both sides.

9/x = 10 - x

(9/x) ⋅ x = (10 - x) ⋅ x         Multiply x on both sides to get rid of the denominator once again.

9 = 10x - x²                       

9 - 9 = 10x -x² -9               Subtract 9 to move everything onto one side.

-x² +10x - 9 = 0                  Rewrite.

-1 (-x² +10x - 9 = 0)           From here, we must factor to get the values of x. But first we must mulitply the equation by -1.

x² - 10x + 9 = 0                  Factor.

(x+10) (x-1) = 0                  Now set each of the parenthesis to equal 0.

x + 10 = 0

x = -10

x - 1 = 0

x = 1

From my perspective, it seems as though the 6th bottle with fill up first.

This is because the water will run to bottle 2 after bottle 1 fills up to the bottom pipe.

And once bottle 2 fills up at the bottom pipe as well, then bottle 6 will fill up first because it will have the most water.

Wow! I didn't know you could solve it like that. You did a good job explaining it. That's very impressive. :) Good job!