On a snow day, Aaron created two snowmen in his backyard. Snowman A was built to a height of 47 inches and Snowman B was built to a height of 59 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 6 inches per hour and Snowman B's height decreased by 8 inches per hour. Let AA represent the height of Snowman A t hours after sunrise and let BB represent the height of Snowman B t hours after sunrise. Write an equation for each situation, in terms of t, and determine the number of hours after sunrise when both snowmen have an equal height.
The equation for the height of Snowman A, AA, t hours after sunrise is:
AA = 47 - 6t
The equation for the height of Snowman B, BB, t hours after sunrise is:
BB = 59 - 8t
To find the number of hours after sunrise when both snowmen have an equal height, we can set AA equal to BB:
47 - 6t = 59 - 8t
Now, let's solve for t:
-6t + 8t = 59 - 47
2t = 12
t = 6
Therefore, both snowmen will have an equal height 6 hours after sunrise.