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On a snow day, Nathan created two snowmen in his backyard. Snowman
A was built to a height of 37 inches and Snowman B was built to a height
of 49 inches. The next day, the temperature increased and both snowmen
began to melt. At sunrise, Snowman A's height decrease by 3 inches per
hour and Snowman B's height decreased by 4 inches per hour. Let A
represent the height of Snowman A t hours after sunrise and let B
represent the height of Snowman B t hours after sunrise. Write an
equation for each situation, in terms of t, and determine how tall each
snowman is when they are the same height.

A=

B=

Answer: ___

Respuesta :

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To solve this problem, we need to write the equations for the height of Snowman A and Snowman B in terms of time (t) after sunrise.

Given information:
- Snowman A's initial height: 37 inches
- Snowman A's height decrease: 3 inches per hour
- Snowman B's initial height: 49 inches
- Snowman B's height decrease: 4 inches per hour

Let's define the variables:
- A: Height of Snowman A (in inches)
- B: Height of Snowman B (in inches)
- t: Time (in hours) after sunrise

Equation for Snowman A:
A = 37 - 3t

Equation for Snowman B:
B = 49 - 4t

To find the time when the two snowmen are the same height, we need to set the two equations equal to each other and solve for t.

A = B
37 - 3t = 49 - 4t
-t = 12
t = 12 hours

Now, we can substitute the value of t into either equation to find the height of the snowmen when they are the same height.

Using the equation for Snowman A:
A = 37 - 3(12)
A = 37 - 36
A = 1 inch

Therefore, when the two snowmen are the same height, they are both 1 inch tall.

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