Question

Roy is a veterinarian at the small-animal clinic. He has 4 appointmentsscheduled for Monday morning two new-patient appointments, a serious injury visiand a dental scaling In hours, how muchtime should these appointments takeNew patient appointment 3/4 hrSerious injury 1 1/4 hrDental scaling 3/4 hra) 2 3/4 b) 3 1/2 c) 3 3/4 or d) 4

Answer 1

Answer

The total time Roy would spend on his 4 appointments is:

$3\frac{1}{2}\text{ hours (OPTION B)}$

Solution

- The question tells us that Roy has 4 appointments: 2 new patients, a serious injury, and dental appointments. We are also given the amount of time (in hours) each category of appointment should take:

New patient appointment 3/4 hr

Serious injury 1 1/4 hr

Dental scaling 3/4 hr

We are asked to find out how long all these appointments would take.

- In order to find how long all the appointments would take, we simply need to add up all the times each scheduled appointment would take.

That is,

$\text{Total time '= Time for 2 New Patients + Time for 1 serious injury + Time for dental appointment}$

- But before we can do this, we should get the times for each appointment.

2 New Patients:

$\begin{gathered} \text{For 1 new patient, the time allotted is }\frac{3}{4}\text{ hours.} \\ \text{Thus, for two new patients, the time allotted would be:} \\ (\frac{3}{4}+\frac{3}{4})\text{hours}=\frac{6}{4}\text{hours} \\ \\ \text{The time allotted for 2 New Patients is }\frac{6}{4}\text{hours} \end{gathered}$

1 Serious Injury:

$\begin{gathered} \text{ For 1 serious injury, the time allotted is }1\frac{1}{4}\text{ hours} \\ \\ \text{Let us convert this mixed fraction to an improper fraction so we can use it for easy calculation:} \\ 1\frac{1}{4}=\frac{(4\times1)+1}{4}=\frac{5}{4}\text{hours} \\ \\ \text{The time allotted for 1 serious injury is }\frac{5}{4}\text{hours} \end{gathered}$

1 Dental appointment:

$\begin{gathered} \text{For 1 dental appointment, the time allotted is }\frac{3}{4}\text{ hours} \\ \\ \text{This is already in its simplest form, thus, we can easily use it for our calculations} \end{gathered}$

- Thus, we can proceed to apply the formula above to find the total amount of time Roy would spend on the 4 appointments.

- This is done below:

$\begin{gathered} \text{Total time '= Time for 2 New Patients + Time for 1 serious injury + Time for dental appointment} \\ \text{Total time}=\frac{6}{4}+\frac{5}{4}+\frac{3}{4}=\frac{6+5+3}{4}=\frac{14}{4}\text{ hours} \\ \\ \text{Converting this time to a Mixed fraction, we have:} \\ \text{Total time}=3\frac{2}{4}\text{ hours}=3\frac{1}{2}\text{ hours} \end{gathered}$

Final Answer

The total time Roy would spend on his 4 appointments is:

$3\frac{1}{2}\text{ hours (OPTION B)}$