Question

Roy is a veterinarian at the small-animal clinic. He has 4 appointmentsscheduled for Monday Morning two new-patient appointments, a serious injury visitand a dental sealing in hours, how muchtime should these appointments take.Sick Animal visit 1/2 hrNew patient Appts : 3/4 hrSerious injury visit 1 1/4 hrdental scaling 3/4 hrImmunizations 1/4 hrRoutine physical 1/3 hr

Answer 1

So we have to find how much time those 4 appointments will take. Since the duration of each appointment is given in fractions it's important to remember a properties of fractions:

$\begin{gathered} \frac{b}{a}+\frac{c}{a}=\frac{b+c}{a} \\ 1=\frac{a}{a} \end{gathered}$

It is also important to remember the relation between the mix number notation and the usual fraction number notation:

$a\text{ }\frac{b}{c}=a+\frac{b}{c}$

With all of this in mind we can start working on the question. The four appointments consist of two 3/4 hr new patient visits, one 1 1/4 hr serious injury visit and one 3/4 hr dental sealing. The time it will take Roy to finish all of them (t) is equal to the sum of their individual times:

$t=\frac{3}{4}+\frac{3}{4}+1\text{ }\frac{1}{4}+\frac{3}{4}$

Using what we saw about mix number notation and fractions we get:

$\begin{gathered} 1\text{ }\frac{1}{4}=1+\frac{1}{4} \\ 1+\frac{1}{4}=\frac{4}{4}+\frac{1}{4}=\frac{4+1}{4}=\frac{5}{4} \\ 1\text{ }\frac{1}{4}=\frac{5}{4} \end{gathered}$

Then we have:

$t=\frac{3}{4}+\frac{3}{4}+\frac{5}{4}+\frac{3}{4}=\frac{3+3+5+3}{4}=\frac{14}{4}=\frac{7}{2}$

So the answer is 7/2 hours.