On a snow day, Aaron created two snowmen in his backyard. Snowman A was built to a height of 28 inches and Snowman B was built to a height of 46 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, commat, and determine the number of hours after sunrise when both snowmen have an equal height.
Question
On a snow day, Aaron created two snowmen in his backyard. Snowman A was built to a height of 28 inches and Snowman B was built to a height of 46 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, commat, and determine the number of hours after sunrise when both snowmen have an equal height.
Solution
Sure, I can help you with that.
Let's start by writing the equations for the height of Snowman A (AA) and Snowman B (BB) at tt hours after sunrise.
For Snowman A: AA = 28 - 4t
For Snowman B: BB = 46 - 7t
To find the number of hours after sunrise when both snowmen have an equal height, we can set AA equal to BB and solve for t:
28 - 4t = 46 - 7t
To solve this equation, we can start by isolating the variable t on one side:
-4t + 7t = 46 - 28
Simplifying the equation gives us:
3t = 18
Now, we can solve for t by dividing both sides of the equation by 3:
t = 18/3
Simplifying further gives us:
t = 6
Therefore, both snowmen will have an equal height 6 hours after sunrise.
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