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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two classmates, Billy and Evelyn, plan to meet in the computer lab to type up their research papers. Billy can type at a speed of page per hour, whereas Evelyn can type pages per hour. So far, Billy already has pages typed up, compared to Evelyn's pages. Once they sit down and start typing together, the two students will reach the same page count before too long. How long will that take? What will the page count be?After hours, each student will have a page count of pages.
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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two classmates, Billy and Evelyn, plan to meet in the computer lab to type up their research papers. Billy can type at a speed of page per hour, whereas Evelyn can type pages per hour. So far, Billy already has pages typed up, compared to Evelyn's pages. Once they sit down and start typing together, the two students will reach the same page count before too long. How long will that take? What will the page count be?After hours, each student will have a page count of pages.
- Define Variables: Let's define the variables:Let be the number of hours they type in the computer lab.Let be the total number of pages each student has after hours.Billy's typing rate is page per hour, and he starts with pages. So, the equation for Billy's total pages after hours is:
- Billy's Equation: Evelyn's typing rate is pages per hour, and she starts with pages. So, the equation for Evelyn's total pages after hours is:
- Evelyn's Equation: Now we have two equations:. (Billy's equation). (Evelyn's equation)Since we are looking for the point where they have the same number of pages, we can set the two equations equal to each other and solve for :
- Set Equations Equal: Subtract from both sides to get the terms on one side:
- Solve for x: Subtract from both sides to isolate the term with :
- Substitute : Divide both sides by to solve for :
- Final Result: Now that we have the value of , we can substitute it back into either equation to find . Let's use Billy's equation:
- Final Result: Now that we have the value of , we can substitute it back into either equation to find . Let's use Billy's equation:We have found that after hours, each student will have a page count of pages.
