Delta Math Functions and graphs word problem

Question

On a snow day, Nakeisha created two snowmen in her backyard. Snowman A was built to a height of 39 inches and Snowman B was built to a height of 60 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 6 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 how tall each snowman is when they are the same height.

Answer 1

The initial height of snowman A is 39 inch and the initial height of snowman B is 60 inch. These are the heights at the time of sunrise. Also, at the time of sunrise, t = 0.

The height of snowman A will reduce by 3 inch every hour. So, after t hours, the height will reduce by 3t inch. So, after t hours, A(t) = 39 - 3t

Similarly, the height of snowman B will reduce by 6 inch every hour. So, after t hours, the height will reduce by 6t inch. So, after t hours, B(t) = 60 - 6t

You can use your calculator or a computer software like Desmos (desmos.com) to graph these functions. The intersection point of the the two graphs (7,18) will give you after how long they will reach the same height and what that height will be. Here, after 7 hours, both will be 18 inch tall.

To solve it analytically, we set,

A(t) = B(t)

⇒ 39 - 3t = 60 - 6t

⇒ 6t - 3t = 60 - 39

⇒ 3t = 21

∴ t = 7 hours.

Plugging in t = 7 in either A(t) or B(t), we get, A(7) = B(7) = 18 inch.