Answer
$0.4\ sec$ and $ 2.1\ sec$
Work Step by Step
Step 1. Given the model function $y=0.6\ sin\frac{2\pi}{5}x$, at $y=0.3\ l/s$ inhaled, we have $0.6\ sin\frac{2\pi}{5}x=0.3$ or $sin\frac{2\pi}{5}x=0.5$
Step 2. The general solution for the above equation is $\frac{2\pi}{5}x=2k\pi+\frac{\pi}{6}$ and $\frac{2\pi}{5}x=2k\pi+\frac{5\pi}{6}$ or $x=5k+\frac{5}{12}$ and $x=5k+\frac{25}{12}$, where $k$ is an integer.
Step 3. Within each breathing cycle of $[0,5)$ seconds, we have $x=\frac{5}{12}\approx0.4\ sec$ and $x=\frac{25}{12}\approx2.1\ sec$
