Need help with linear equations

Question

1. Ms. Schiedler’s friend decided to run a marathon (26.2 mi) for the first time with a goal of finishing the race. They ran for part of the race and walked the rest. Their average running rate is 11.5 miles per hour and their average walking pace is 3.75 miles per hour and they finished the race in 3.82 hours. At the end, they wanted to know how much time they spent running and how much time they spent walking. 

Let x=time spent running

Let y = time spent walking

1. Write a system of two equations to model this problem. Describe what each equation represents.
2. Solve the system of equations using either substitution or elimination.
3. Check your solution

Answer 1

distance = speed times time

d = st

11.5x + 3.75y = 26.2

x +y = 3.82

3.75x + 3.75 = 3.75(3.82) = 14.325

(11.5 -3.75)x = 26.2 -14.325 = 11.875

x= 11.875/7.75 = about 1.532 hours running

y = 2.288 hours walking

11/5(1.532) + 3.75(2.288) = 17.62 + 8.58 = 26.2 miles total

ran 17.62 miles, walked 8.58 miles