Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
two classmates, judith and debbie, plan to meet in the computer lab to type up their research papers. judith can type at a speed of 1 page per hour, whereas debbie can type 2 pages per hour. so far, judith already has 13 pages typed up, compared to debbie’s 12 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 (\boxed{}) hours, each student will have a page count of (\boxed{}) pages.
submit

Explanation:

Step1: Define variables for time and pages

Let $t$ = time (in hours) spent typing together, $J$ = Judith's total pages, $D$ = Debbie's total pages.

Step2: Write equations for total pages

Judith: $J = 13 + 1t$
Debbie: $D = 12 + 2t$

Step3: Set equations equal (same page count)

$13 + t = 12 + 2t$

Step4: Solve for $t$

Subtract $t$ and 12 from both sides:
$13 - 12 = 2t - t$
$1 = t$

Step5: Calculate total page count

Substitute $t=1$ into Judith's equation:
$J = 13 + 1(1) = 14$

Answer:

After 1 hours, each student will have a page count of 14 pages.