Answer:
[tex]11 \frac{3}{4}[/tex] min
Step-by-step explanation:
In order to solve this problem, we must subtract the times he has already used from the time he has available, so we get:
[tex]30-11 \frac{3}{4} - 6 \frac{1}{2}[/tex]
we can start solving this subtraction by turning all of the numbers into improper fractions so we get:
[tex]\frac{30}{1}-\frac{11*4+3}{4}- \frac{6*2+1}{2}[/tex]
[tex] \frac{30}{1}-\frac{47}{4}- \frac{13}{2}[/tex]
next, we can find a least common denominator. In this case it will be 4, so we need to turn all denominators into a 4, so we get:
[tex] \frac{30*4}{1*4}-\frac{47}{4}- \frac{13*2}{2*2}[/tex]
[tex] \frac{120}{4}-\frac{47}{4}- \frac{26}{4}[/tex]
and now we can subtract the numerators and copy the denominators so we get:
[tex]\frac{120-47-26}{4}[/tex]
[tex]\frac{47}{4}[/tex]
which can now be turned into a mixed number by dividing 47/4 which yields 11 with a remainder of 3, so the mixed number is:
[tex]11 \frac{3}{4}[/tex] min
and this is the amount of time he has available to solve the las problem.
