Question

the international swimming hall of fame and museum is in fort lauderdale, florida. the olympic - qualifying time for the 50 m freestyle is 24.77 seconds. aj decides to work towards qualifying for the olympics and finds that her time can be improved by practicing more. after several months of practice, she determines that the equation a=-0.025cdot h + 26.5 models her average time (a) in terms of how many hours (h) she practices in a week. if aj practices 12 hours in a week, she can expect to have an average time of the inequality 24.77>-0.025cdot h + 26.5 can be used to determine how many hours a week she needs to practice to be under the qualification time. aj needs to train more than hours in order to qualify. complete the following statements.

Explanation:

Step1: Rearrange the inequality

We start with the inequality \(21.77>- 0.025h + 26.5\). First, subtract 26.5 from both sides. So, \(21.77 - 26.5>-0.025h+26.5 - 26.5\), which simplifies to \(-4.73>-0.025h\).

Step2: Solve for \(h\)

When we divide both sides of the inequality \(-4.73>-0.025h\) by - 0.025, we need to reverse the inequality sign (since we are dividing by a negative number). So, \(\frac{-4.73}{-0.025}<\frac{-0.025h}{-0.025}\), and \(h > 189.2\).

Answer:

\(h>189.2\)