Question

On a snow day, Caroline created two snowmen in her backyard. Snowman A was built

to a height of 36 inches and Snowman B was built to a height of 57 inches. The next
day, the temperature increased and both snowmen began to melt. At sunrise,
Snowman A's height decrease by 3 inches per hour and Snowman B's height
decreased by 6 inches per hour. Let A represent the height of Snowman At hours
after sunrise and let B represent the height of Snowman Bf hours after sunrise.
Graph each function and determine how tall each snowman is when they are the
same height.

Answer 1

Explanation:

We can start by setting up equations for the height of each snowman as a function of time. Let t be the time in hours after sunrise.

For Snowman A, the height as a function of time is given by:

A(t) = 36 - 3t

For Snowman B, the height as a function of time is given by:

B(t) = 57 - 6t

To find when the two snowmen are the same height, we can set the two equations equal to each other and solve for t:

36 - 3t = 57 - 6t

3t = 21

t = 7

So the two snowmen will be the same height after 7 hours.

To find the height of each snowman at that time, we can substitute t = 7 into the equations:

A(7) = 36 - 3(7) = 15 inches

B(7) = 57 - 6(7) = 15 inches

Therefore, both Snowman A and Snowman B will be 15 inches tall after 7 hours.

To graph the functions, we can plot points for various values of t and connect them with a straight line:

For A(t):

t | A(t)

--|-----

0 | 36

1 | 33

2 | 30

3 | 27

4 | 24

5 | 21

6 | 18

7 | 15

For B(t):

t | B(t)

--|-----

0 | 57

1 | 51

2 | 45

3 | 39

4 | 33

5 | 27

6 | 21

7 | 15

The graph of both functions is a straight line with a negative slope. The two lines intersect at (7, 15), which represents the point in time when both snowmen are the same height.