Sure, let's break this problem down step by step to find the number of practice sets Javier can do.
1. Total Practice Duration:
Javier's swim practice lasts for [tex]\(1 \frac{1}{2}\)[/tex] hours. Converting this to an improper fraction, we get:
[tex]\[
1 \frac{1}{2} = \frac{3}{2} \text{ hours}
\][/tex]
2. Stretching Time:
The team spends [tex]\(\frac{1}{6}\)[/tex] of an hour stretching.
3. Practice Duration After Stretching:
To find the time left for practice sets after stretching, we subtract the stretching time from the total practice duration:
[tex]\[
\frac{3}{2} - \frac{1}{6}
\][/tex]
First, we need a common denominator to subtract these fractions. The common denominator for 2 and 6 is 6. Converting both fractions:
[tex]\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
\][/tex]
Now we subtract:
[tex]\[
\frac{9}{6} - \frac{1}{6} = \frac{9 - 1}{6} = \frac{8}{6} = \frac{4}{3} \text{ hours}
\][/tex]
4. Time for Each Practice Set:
Each practice set takes [tex]\(\frac{1}{3}\)[/tex] of an hour.
5. Number of Practice Sets:
To find how many practice sets Javier can complete in the remaining time, we divide the time left by the time per set:
[tex]\[
\text{Number of sets} = \frac{\frac{4}{3}}{\frac{1}{3}}
\][/tex]
Dividing fractions means we multiply by the reciprocal:
[tex]\[
\frac{4}{3} \times \frac{3}{1} = \frac{4 \times 3}{3 \times 1} = \frac{12}{3} = 4
\][/tex]
Therefore, Javier can do [tex]\(4\)[/tex] practice sets before the practice is over.
