Let's begin by setting up equations for the heights of Snowman A and Snowman B.

Snowman A:

• Initially, Snowman A has a height of 55 inches.
• Every hour, the height of Snowman A decreases by 5 inches.

Thus, the height of Snowman A after $t$ hours can be represented by the equation: $A(t) = 55 - 5t$

Snowman B:

• Initially, Snowman B has a height of 34 inches.
• Every hour, the height of Snowman B decreases by 2 inches.

Thus, the height of Snowman B after $t$ hours can be represented by the equation: $B(t) = 34 - 2t$

Determine which Snowman is taller after 5 hours:

Now, we will substitute $t = 5$ into both equations to find the heights after 5 hours.

For Snowman A: $A(5) = 55 - 5(5) = 55 - 25 = 30 \, \text{inches}$

For Snowman B: $B(5) = 34 - 2(5) = 34 - 10 = 24 \, \text{inches}$

Conclusion:

After 5 hours, Snowman A is taller at 30 inches, while Snowman B is 24 inches tall.

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Would you like further details on how these equations were created? Here are 5 related questions that might interest you:

1. How would the equation change if Snowman A melted at a rate of 3 inches per hour instead of 5?
2. What would be the height of both snowmen after 8 hours?
3. How could we graph the equations of the snowmen's heights over time?
4. If the snowmen melted at the same rate, how would their heights compare after several hours?
5. What would happen if the initial height of Snowman B was greater than Snowman A?

Tip: When solving word problems like this, always start by identifying the initial values and the rates of change before forming your equation.