Question

Two classmates got together over the weekend to do their assigned History reading. Jayla can read 3 pages per minute, while Ellie can read 4 pages per minute. When they met, Jayla had already read 100 pages, and Ellie had already gotten through 50 pages. After a while, they had both read the same number of pages. How long did that take? Write a system of equations, graph them, and type the solution.

Answer 1

Jayla and Ellie, with reading speeds of 3 and 4 pages per minute respectively, met after Jayla had read 100 pages and Ellie had read 50 pages. It took them 50 minutes to read an equal number of pages, with each having read 250 pages in total.

Let x be the time in minutes it took for them to read the same number of pages. Jayla had read 100 + 3x pages, and Ellie had read 50 + 4x pages. The system of equations is:

100 + 3x = 50 + 4x

To solve, subtract 3x from both sides:

100 = 50 + x

Then, subtract 50 from both sides:

x = 50

So, it took 50 minutes for Jayla and Ellie to read the same number of pages. In terms of the number of pages, Jayla read 100 + 3 * 50 = 250 pages, and Ellie read 50 + 4 * 50 = 250 pages as well. The solution can be graphically represented by the point (50, 250) on the coordinate plane.