On a snow day, Jin created two snowmen in his backyard. Snowman A was built to a height of 40 inches and Snowman B was built to a height of 26 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 2 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. Graph each function and determine which Snowman is taller after 4 hours.

Answer 1

To find the heights of Snowman A and Snowman B after \( tt \) hours since sunrise, we can establish mathematical functions based on the problem:

1. Snowman A:

   • Initial height = 40 inches
   • Height decrease = 4 inches per hour

   The function for the height of Snowman A after \( tt \) hours is: \[ AA = 40 - 4tt \]

2. Snowman B:

   • Initial height = 26 inches
   • Height decrease = 2 inches per hour

   The function for the height of Snowman B after \( tt \) hours is: \[ BB = 26 - 2tt \]

Next, we can substitute \( tt = 4 \) into both functions to find the height of each snowman after 4 hours:

For Snowman A: \[ AA = 40 - 4(4) = 40 - 16 = 24 \text{ inches} \]

For Snowman B: \[ BB = 26 - 2(4) = 26 - 8 = 18 \text{ inches} \]

Now, we can compare the heights of both snowmen after 4 hours:

• Height of Snowman A after 4 hours = 24 inches
• Height of Snowman B after 4 hours = 18 inches

Conclusion

After 4 hours, Snowman A (24 inches) is taller than Snowman B (18 inches).