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.

Answer 1

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.