Algebra question FPS

Question

Hannah and Nora started running down opposite sides of a hallway 100ft long heading toward one another. They ran into each other 5 seconds after they started. If Hannah ran 4 feet per second faster than Nora, how fast was Hannah running in terms of feet per second

Answer 1

Distance = Rate x Time

Total distance = 100 ft Hannah's speed = H Nora's speed = N

Time for each is 5 sec.

H = N + 4

H's distance = 5(H) N's distance = 5(N)

H's distance + N's distance = 100

5H + 5N = 100 but H = N + 4

Substituting: 100 = 5(N + 4) + 5N -> 100 = 5N + 20 + 5N

80 = 10N N = 8 fps, so H = 12 fps

Check: Hannah goes 12(5) = 60 ft

Nora goes 8(5) = 40 ft.

Total 100 ft.