Answer:
8 weeks, 9 miles
Step-by-step explanation:
If y=(1/2)x+5 and y=(3/4)x+3, then you can set both equations equal to each other and solve for x:
(1/2)x+5=(3/4)x+3.
Subtract 3 from both sides:
(1/2)x+2=(3/4)x. Next, subtract (1/2)x from each side. This leaves you with 2=(1/4)x. To get rid of a fraction, multiply both sides by its reciprocal (1/4-->4/1, or 4). 2 times 4=8, so x=8. So for the total mileage to be the same, Cora and Hana must run for 8 weeks. To find their common mileage at that point, just plug 8 for x in one of the equations (you should get the same y value no matter which one you use):
y=(1/2)x+5
y=(1/2)8+5
y=4+5
y=9
So Cora and Hana must run for 8 weeks in order for their total mileage, 9 miles, to be the same.
Also, you might want to check your graph for y=(3/4)x+3. After 4 weeks, the total mileage should be 6 miles, not 4. You can find each y value by either plugging in x (weeks) into the equation (y=(3/4)(4)+3, so y=6) or you can start at the y-intercept, 3, which you already did, and just count 3 up on the y axis and 4 to the right on the x axis.
