Final answer:
To determine the walking speed on a nonmoving sidewalk, we solved the equation based on times being equal for different distances on a moving sidewalk. The calculations revealed the walking speed to be 2.9 ft/sec.
Step-by-step explanation:
The question involves determining the walking speed of a person on a nonmoving sidewalk based on given times to cover certain distances on a moving sidewalk at a known speed. Let's denote the person's walking speed on the nonmoving sidewalk as x ft/sec.
When the person moves with the moving sidewalk, their effective speed is (x + 1.9) ft/sec, because both the sidewalk and the person are moving in the same direction. We can calculate the time it took to travel 104 ft using the formula time = distance / speed, which in this case is t1 = 104 / (x + 1.9).
In the opposite direction, against the moving sidewalk, the effective speed is (x - 1.9) ft/sec. The time it took to travel the 52 ft is t2 = 52 / (x - 1.9). Since the times are the same, we have t1 = t2.
Setting the equations equal to each other gives us:
- 104 / (x + 1.9) = 52 / (x - 1.9)
Multiplying both sides by (x + 1.9)(x - 1.9) to remove the denominators, we get:
- 104(x - 1.9) = 52(x + 1.9)
After expanding and simplifying, we find that x, the walking speed on the nonmoving sidewalk, is 2.9 ft/sec.