Javier's swim practice is 1
1
2
hours long. The team spends
1
6
of an hour stretching before they start their practice sets. If each practice set takes
1
3
of an hour, how many sets can Javier do before practice is over?
To find out how many sets Javier can do before practice is over, we need to subtract the time spent on stretching from the total practice time.
The time spent on stretching is 1/6 hours.
So, the remaining practice time is 1 hour - 1/6 hours = (6/6 - 1/6) hours = 5/6 hours.
Each practice set takes 1/3 hours.
To find out how many sets can be done in 5/6 hours, we divide 5/6 hours by 1/3 hours.
When we divide a fraction, we can simplify it by multiplying the numerator by the reciprocal of the denominator.
So, 5/6 hours divided by 1/3 hours can be written as 5/6 * 3/1 = (5*3)/(6*1) = 15/6.
We can simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.
So, 15/6 = (15/3) / (6/3) = 5/2.
Therefore, Javier can do 5/2 sets before practice is over.
Since 5/2 is an improper fraction, we can convert it to a mixed number by dividing the numerator (5) by the denominator (2).
So, 5/2 = 2 and 1/2.
Therefore, Javier can do 2 sets and 1/2 set before practice is over.
To find out how many sets Javier can do before practice is over, we need to subtract the time spent stretching from the total practice time and then divide by the time taken for each practice set.
Step 1: Subtract the time spent stretching from the total practice time:
Total practice time - Time spent stretching = Actual practice time
2 hours - (1/6) hour = (12/6) - (1/6) = (11/6) hours
Step 2: Divide the actual practice time by the time taken for each practice set:
(11/6) ÷ (1/3)
When we divide a fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.
(11/6) × (3/1) = (11/2) = 5.5
Therefore, Javier can do 5.5 practice sets before practice is over. Since we cannot have half of a practice set, Javier can do a maximum of 5 practice sets before practice is over.