The speed of a moving sidewalk at an airport is 3 ft/sec. A person can walk 79 ft forward on the moving sidewalk in the same time it takes to walk 15 ft on a nonmoving sidewalk in the opposite direction. At what rate would a person walk on a nonmoving sidewalk?
looooooooool idk
(r + 3) / 79 = r / 15
15 r + 45 = 79 r
To solve this problem, let's assume the rate at which a person walks on a nonmoving sidewalk is "x ft/s."
Let's consider the scenario where a person walks on the moving sidewalk. The speed of the moving sidewalk is given as 3 ft/s, and the person walks 79 ft forward. The time taken to cover this distance is the same as the time taken to walk 15 ft on a nonmoving sidewalk in the opposite direction.
Using the formula distance = rate x time, we can set up the two equations:
Distance on moving sidewalk = Rate on moving sidewalk x Time
79 ft = (3 ft/s + x ft/s) x Time (1)
Distance on nonmoving sidewalk = Rate on nonmoving sidewalk x Time
15 ft = (x ft/s) x Time (2)
Now, we need to find the value of x using these equations.
From equation (2), we can express time in terms of distance and rate:
Time = Distance on nonmoving sidewalk / Rate on nonmoving sidewalk
Time = 15 ft / x ft/s
Substituting this value of time into equation (1), we get:
79 ft = (3 ft/s + x ft/s) x (15 ft / x ft/s)
Simplifying further:
79 ft = (3 ft/s + x ft/s) * (15 ft / x ft/s)
79 ft = (45 ft/s + 15x ft/s) / x ft/s
To eliminate the units of ft/s, we multiply both sides by x ft/s:
79 ft * x ft/s = 45 ft/s + 15x ft/s
Now, we have an equation without units:
79x = 45 + 15x
Simplifying the equation, we isolate the x term:
79x - 15x = 45
64x = 45
To solve for x, divide both sides by 64:
x = 45 / 64
Therefore, the rate at which a person will walk on a nonmoving sidewalk is approximately 0.703 ft/s.