On a snow day, Brooklyn created two snowmen in her backyard. Snowman A was built to a height of 60 inches and Snowman B was built to a height of 44 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 5 inches per hour and Snowman B's height decreased by 3 inches per hour. Let A(t)A(t) represent the height of Snowman A tt hours after sunrise and let B(t)B(t) represent the height of Snowman B tt hours after sunrise. Write the equation for each function and determine the number of hours after sunrise when both snowmen have an equal height.

The rate at which the height of each snowman decreased is linear. This means that it was decreasing in arithmetic progression. The formula for determining the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference

n represents the number of terms(hours)

Considering snowman A,

Tn = A(t)

n = t

a = 60 inches

d = - 5 inches(since it is decreasing)

Therefore,

A(t) = 60 + (t - 1)-5

A(t) = 60 - 5t + 5

A(t) = 65 - 5t

Considering snowman B,

Tn = B(t)

n = t

a = 44 inches

d = - 3 inches(since it is decreasing)

Therefore,

B(t) = 44 + (t - 1)-3

B(t) = 44 - 3t + 3

B(t) = 47 - 3t

For both snowmen to have an equal height, it means that

65 - 5t = 47 - 3t

- 5t + 3t = 47 - 65

- 2t = - 18

t = - 18/- 2

t = 9 hours