Question

2. The height of a swimmer’s dive off a 10-foot high platform into a pool is modeled by the equation y=2x2-16x+24, where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water’s surface. A turtle was hanging out by the pool working on his tan. He decided to swim down into the pool because he saw a shiny object at the bottom. His path is modeled by y = -x - 1. For how long did the swimmer dive below the turtle?

Answer 1

Solution

We have the following expression:

$y=2x^2-16x+24$

y= height of the pool and x= time in seconds

And we know that the turtle path is given by:

$y=-x-1$

We can do the following:

$2x^2-16x+24<-x-1$

And we can solve for x on this way:

$2x^2-15x+25<0$

We can factorize and we got:

$(2x-5)(x-5)<0$

And we can do the following to solve the problem:

Then we can conclude that the answer is:

5/2 < x < 5

Between 5/2 and 5 seconds the swimmer dive is below the turtle that represent 5/2 seconds