Solve a system of equations by graphing: word problems

Question

Two classmates, Lucia and Rosa, plan to meet in the computer lab to type up their research papers. Lucia can type at a speed of 1 page per hour, whereas Rosa can type 2 pages per hour. So far, Lucia already has 7 pages typed up, compared to Rosa's 5 pages. Once they sit down and start typing together, the two students will reach the same page count before too long. What will the page count be?

Answer 1

Hi Layanna,

This long answer may explain how to think of these “combined work” problems.

Let L (= 1) be Lucia’s rate, pages per hour

Let R (= 2) be Rosa rate

Let T be typing time Together

Pages = Rate x Time, abbreviated:

P = (R + L) x T

Lucia’s pages = 7 + LT 

Rosas pages = 5 + RT 

Total typing time together = time where Lucia’s pages = Rosa’s pages

7 + LT = 5 + RT

Substitute known rates L and R

7 + T = 5 + 2T

Solve for T

7-5 = 2 T - T

T = 2 hours

Total page count = 

7 + 2 + 5 + 4 = 18

Answer 2

y lucia = x+7

y rosa = 2x+5

2x+5=x+7, x=2