On a snow day, Nolan created two snowmen in his backyard. Snowman A was built to a height of 31 inches and Snowman B was built to a height of 52 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 4 inches per hour and Snowman B's height decreased by 7 inches per hour. Let AA represent the height of Snowman A tt hours after sunrise and let BB represent the height of Snowman B tt hours after sunrise. Write an equation for each situation, in terms of t, t, and determine the interval of time, t, t, when Snowman A is taller than Snowman B.

An equation for each situation

A = 31 - 4t

B = 52 - 7t

The interval of time, t,, when Snowman A is taller than Snowman B is t > 7 hours i.e

The interval of time, t, when Snowman A is taller than Snowman B is from

7.01 hours and above.

Step-by-step explanation:

Let t represent the number of hours at which the snow melts

Let A represent the height of Snowman A t hours after sunrise

Let B represent the height of Snowman B tt hours after sunrise.

An equation for each situation

A = 31 - 4(t)

B = 52 - 7(t)

The interval of time, t, when Snowman A is taller than Snowman B.

A > B

31 - 4t > 52 - 7t

Collect like terms

-4t + 7t > 52 - 31

3t > 21

t > 21/3

t > 7

This means after 7 hours, Snowman A is taller Snowman B

The interval of time, t, when Snowman A is taller than Snowman B is from

7.01 hours and above.