Question

One student begins in Cleveland, Ohio, and walks towards Buffalo, New York, a distance of 200 miles. She walks at the rate of 2.5 miles per hour. Another student begins riding his bicycle in Cleveland and rides towards Buffalo at the rate of 11 miles per hour. The walking student begins her journey at 8:00 AM. The riding student starts 4 hours later.

Part A Write a system of two equations that could be used to find the distance each student is from Cleveland, Ohio, at any given time. Let x represent the distance that the walking student is from Cleveland, let y represent the distance that the riding student is from Cleveland, and let t be the time that has elapsed since the walking student left Cleveland.

Part B Solve the system of equations for x and y to determine how many hours elapse before the students meet.

Answer 1

ok so student in cleveland walks 2.5 miles away from cleveland every hour from 8
so the distance, x is x=2.5t

the riding one rides 4 hours later, so t-4
11 mph
y=11(t-4)

A. x=2.5t
y=11(t-4)

when do they meet is when the distance when they are equal or when x=y
2.5t=x=y=11(t-4)
solve for t
2.5t=11(t-4)
2.5t=11t-44
-8.5t=-44
divide both sides by -8.5
t=5.17647

answer is 5.18 hours


A.
x=2.5t
y=11(t-4)

B. 5.18 hours