Question

at the end of the school year, Rachel and Amber go to the roof of a 12-story building and throw their Algebra book off the edge. the equation of the pathway that each girl's textbook takes is given below. by how many seconds does Rachel's textbook beat Amber's to the ground?

Answer 1

Answer:
`By\ 0.6\ seconds`

Explanation:

The missing equations are:

`Rachel: \\h=-16t^2+36t+160\\Amber: \\h=-16t^2+50t+160`

Make each equation equal to 0 and then apply the the Quadratic formula
`x=(-b\±√(b^2-4ac) )/(2a)`

Time it takes Rachel's textbook to reach the ground (in seconds)

Having the equation:

`0=-16t^2+36t+160`

We can identify that:

`a=-16\\b=36\\c=160`

Substituting values into the Quadratic formula, we get:

`x=(-36\±√((36)^2-4(-16)(160)) )/(2(-16))\\\\x_1=4.48\\\\x_2=-2.23`

Time it takes Amber's textbook to reach the ground (in seconds)

Having the equation:

`0=-16t^2+50t+160`

We can identify that:

`a=-16\\b=50\\c=160`

Substituting values into the Quadratic formula, we get:

`x=(-50\±√((50)^2-4(-16)(160)) )/(2(-16))\\\\x_1=5.08\\\\x_2=-1.96`

The difference of the positive values is:

`5.08\ seconds-4.48\ seconds=0.6\ seconds`

Therefore, Rachel's textbook beat Amber's to the ground by
`0.6\ seconds`