Graphing System of equations

Question

Ken and Kayla are reading a book . Ken is already on page 9 and reads a page every 2 minutes. Kayla has just started reading and can finish a page in just half a minute . After how many minutes will ken and Kayla have the same number of pages read?

Answer 1

You will need to write an expression for their page position for both Ken and Kayla, then set those two expressions equal to each other and solve for x.

Each of the two expressions will be the right side of a linear equation with form y = mx + b.

y is the current page.

x is the number of minutes from the start time (now).,

m is the slope. That is a rate. For this situation the rate will be pages per minute. (Notice that this is y units per x unit).

b is called the y-intercept. That is the the initial value of y. Initial value means y when x = 0.

Let's start with Ken.

He's already on page nine when we start counting time. (x=0) so 9 is the initial value:. b=9.

Ken's rate is 2 minutes per page. But we need pages per minute. That's just the reciprocal of 2. m = 1/2 = 0.5 pages/minute.

The expression for Ken's current page is y=mx+b, of y = 0.5x + 9.

Kayla is just starting so her initial value is page number zero: b = 0, so we can just leave it out of our expression.

Kayla takes half a minute to read a page. That's 0.5 minutes per page, or 2 pages per minute. m=2.

Her expression is y = 2x. (Remember, her b is zero. We don't need to add a zero: y=2x+0.

Now we set one expression equal to the other. Just put an equals sign between them and solve for x.

2x = 0.5x + 9 subtract 0.5x from both sides

2x - 0.5x = 0.5x - 0.5x + 9

1.5x = 9 divide both sides by 1.5

x=6