Question

On a snow day, Faith created two snowmen in herbackyard. Snowman A was built toa height of 34 inches and Snowman B was built toa height of 24 inches. The next day,the temperature increased and both snowmenbegan to melt. At sunrise, SnowmanA's height decrease by 6 inches per hour andSnowman B's height decreased by 4inches per hour. Let A represent the height ofSnowman At hours after sunrise andlet B represent the height of Snowman Bt hoursafter sunrise. Graph each functionand determine the interval of time, t, whenSnowman A is taller than Snowman B.so below is the graph i have right now and theapp for no reason disconnected me from mytutor so i cant ask him if its right and i just needconfirmation if this is right or wrong and if itswrong, where the lines should be instead

Answer 1

Snowman A was built to a height of 34 inches

At sunrise, Snowman A's height decrease by 6 inches per hour

Let A represent the height of Snowman At hours after sunrise

$A=34-6t$

Snowman B was built to a height of 24 inches

At sunrise, Snowman B's height decrease by 4 inches per hour

Let B represent the height of Snowman Bt hours after sunrise

$B=24-4t$

When Snowman A is taller than Snowman B?

When A is greater than B

$\begin{gathered} A>B \\ 34-6t>24-4t \\ -6t+4t>24-34 \\ -2t>-10 \\ 2t<10 \\ t<\frac{10}{2} \\ t<5 \end{gathered}$

This means that for t less than 5 hours, Snowman A is taller than Snowmen B

Let us have a look at the graph of both lines

The red line is Snowmen A and the green line is Snowmen B

The point of intersection is at t = 5 (the height of both Snowmen at this point is 4 inches)

Before t = 5, Snowmen A is taller than Snowmen B

After t = 5, Snowmen B is taller than Snowmen A

Therefore, the time interval when Snowman A is taller than Snowman B is between 0 and 5 hours

$t=(0,5)$