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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Two students in Mr. Terry's class, Britney and Francesca, have been assigned a workbook to complete at their own pace. They get together at Britney's house after school to complete as many pages as they can. Britney has already completed pages and will continue working at a rate of pages per hour. Francesca has completed pages and can work at a rate of pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed?After hours, Britney and Francesca will have each completed pages in their workbooks.
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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Two students in Mr. Terry's class, Britney and Francesca, have been assigned a workbook to complete at their own pace. They get together at Britney's house after school to complete as many pages as they can. Britney has already completed pages and will continue working at a rate of pages per hour. Francesca has completed pages and can work at a rate of pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed?After hours, Britney and Francesca will have each completed pages in their workbooks.
- Define Variables: Let's define the variables:Let be the time in hours after Britney and Francesca start working at Britney's house.Let be the total number of pages Britney will have completed after hours.Let be the total number of pages Francesca will have completed after hours.We can write two equations to represent the situation:For Britney: (since she has already completed pages and works at a rate of pages per hour).For Francesca: (since she has already completed pages and works at a rate of pages per hour).We want to find the time when equals , which means Britney and Francesca will be working on the same page.
- Set Up Equations: Now we set up the equations to find when equals :To solve for , we need to get all the terms with on one side and the constant terms on the other side. Subtract from both sides:
- Solve for t: Next, we subtract from both sides to isolate the term with : Now we divide both sides by to solve for :
- Calculate Pages Completed: We have found that hours. Now we need to calculate how many pages each student will have completed after hours.For Britney:For Francesca:
- Final Result: We have found that after hours, both Britney and Francesca will have completed pages each in their workbooks.
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