Question

At 9 a.m., Jessica started riding on the Red Mountain Parkway at the 40-mile marker.

At the same time, Kate started riding on the Red Mountain Parkway at the 10-mile
marker. Jessica rides her motorcycle at a rate of 30 miles per hour. Kate rides her
motorcycle at a rate of 40 miles per hour. If they are both riding in the same direction,
which graph shows the number of hours after 9 a.m. when Jessica and Kate will be in
the same position on the parkway?

Answer 1

See below

Explanation:

Start time = 9 A.M.

Jessica

• Start point- 40 miles
• Speed - 30 mph

Equation:

• y = 40 + 30x

Kate

• Start point- 10 miles
• Speed - 40 mph

Equation:

• y = 10 + 40x

Note. There is no graph but see the attached. It should be similar graph for this case

The will meet after 3 hours at 130 miles mark

Solving the system of equations we get:

• 40+30x = 10 + 40x
• 10x = 30
• x = 3

And y is:

• y = 40+3*30 = 130

(3, 130) is the intersection of lines

Since it takes 3 hours for Jessica and Kate, it happens at 12 A.M.