There are 10 hours and 15 minutes between 7:30AM and 5:45PM.
Since Roger gets a 50 minute lunch break and two 20 minute breaks, we can add all of the breaks together and subtract the total break time from his work time.
![50 + 2(20) = 50 + 40 = 90](https://img.qammunity.org/2019/formulas/mathematics/middle-school/t7f4sdssnob7sb0u4hlc7ti2pfno9f167y.png)
Convert 10 hours, 15 minutes into minutes. There are 60 minutes in an hour.
![10(60) + 15 = 600 + 15 = 615](https://img.qammunity.org/2019/formulas/mathematics/middle-school/vnoikkd1klbx6fu002uekqn1121evjchls.png)
Subtract the total break time from the total minutes during Roger's work day.
![615 - 90 = 525](https://img.qammunity.org/2019/formulas/mathematics/middle-school/8knce1a77q1c1gqc5kltz9ce8l6o59s78z.png)
Convert this number into hours and minutes.
![525 / 60 = 8 R45](https://img.qammunity.org/2019/formulas/mathematics/middle-school/4yxtz2ptvcgo0r0tzxn9yg0uzwyl8ltu00.png)
R45 represents the minutes.
Roger works
8 hours and 45 minutes every work day.