Walking down a long moving escalator, Phil covered 75 m in distance in 25 seconds. Walking back up against the motion of the escalator, the distance was covered in 75 seconds. What was the speed of the escalator?
V = Vmax - Vmin,
V = 75m / 25s - 75m / 75s = 3 - 1 = 2m/s.
To find the speed of the escalator, let's analyze the problem:
Let's assume Phil's walking speed is V and the speed of the escalator is E.
When Phil is walking down the escalator, his effective speed is the sum of his walking speed and the speed of the escalator. So, his effective speed is (V + E).
When Phil is walking up against the motion of the escalator, his effective speed is the difference between his walking speed and the speed of the escalator. So, his effective speed is (V - E).
We are given two pieces of information:
1. When Phil walks down the escalator, he covers a distance of 75 meters in 25 seconds. So, the equation is:
Distance = Speed × Time
75 = (V + E) × 25
2. When Phil walks up against the motion of the escalator, he covers the same distance of 75 meters in 75 seconds. So, the equation is:
Distance = Speed × Time
75 = (V - E) × 75
Now, we have two equations with two unknowns (V and E). Let's solve them simultaneously.
From the first equation, we can isolate V + E:
V + E = 75 / 25
V + E = 3
From the second equation, we can isolate V - E:
V - E = 75 / 75
V - E = 1
Now, let's solve these two equations by adding them together:
(V + E) + (V - E) = 3 + 1
2V = 4
V = 2
Now that we have the value of V, we can substitute it into either of the initial equations to find E:
V + E = 3
2 + E = 3
E = 3 - 2
E = 1
Therefore, the speed of the escalator is 1 meter per second.