walking down a long moving escalator, phil covered the 75 m distance in 25 s. walking back up against the motion of the escalator, the same distance was covered in 75 s. what is the speed of the escalator?
Letting Vw = Phil's walking speed and Ve = the escalator's speed;
Vw + Ve = 75/25 = 3m/s
Vw - Ve = 75/75 = 1m/s
Adding,
2Vw = 4 making Vw = 2m/s and Ve = 1m/s.
When Anthony went bass fishing, he rowed 4 km against the current in 2 hr. On his return trip, he still had 1 km to go to his starting point after he had been traveling for 0.5 hr. Find Anthony's rate of rowing in still water and the speed of the current.
To find the speed of the escalator, we need to first determine the speed at which Phil walks in still air.
Let's denote the speed at which Phil walks in still air as x m/s and the speed of the escalator as y m/s.
When Phil walks down the escalator, the effective speed is the sum of his walking speed and the speed of the escalator.
Therefore, when Phil walks down, the effective speed is (x + y) m/s.
Using the formula distance = speed × time, we have:
Distance covered when walking down = (x + y) × 25 m ... (1)
Similarly, when Phil walks up against the escalator, the effective speed is the difference between his walking speed and the speed of the escalator.
Therefore, when Phil walks up, the effective speed is (x - y) m/s.
Using the same formula, we have:
Distance covered when walking up = (x - y) × 75 m ... (2)
Given that the distance covered is the same in both cases (75 m), we can equate equations (1) and (2):
(x + y) × 25 = (x - y) × 75
Expanding the equation:
25x + 25y = 75x - 75y
Move all the terms with x to one side:
25x - 75x = 75y - 25y
-50x = 50y
Divide both sides by 50:
x = y
This suggests that the speed at which Phil walks in still air (x) is equal to the speed of the escalator (y).
Since Phil covered a distance of 75 meters in 25 seconds when walking down the escalator, we can find the value of x (and y) using this information:
x + y = 75/25 = 3
Since x = y, we can write:
2x = 3
Divide both sides by 2:
x = 3/2 = 1.5 m/s
So, the speed of the escalator (y) is also 1.5 m/s.
To find the speed of the escalator, we need to analyze the different scenarios provided:
1. When Phil walks down the escalator:
- Let's assume Phil's walking speed is 'v' m/s.
- Since the escalator is moving in the same direction, the total speed would be the sum of Phil's walking speed and the speed of the escalator.
- The distance covered is 75 m, and the time taken is 25 s.
- Using the formula distance = speed x time, we can write: 75 = (v + E) x 25, where E is the speed of the escalator.
2. When Phil walks back up against the motion of the escalator:
- When Phil walks against the escalator, the total speed will be the difference between his walking speed and the speed of the escalator.
- Again, using the distance = speed x time formula, we have 75 = (v - E) x 75.
Now, we have two equations:
1. 75 = (v + E) x 25
2. 75 = (v - E) x 75
We can solve this system of equations to find the values of v (Phil's walking speed) and E (escalator speed).
Let's solve the equations:
1. Expanding equation 1, we get: 75 = 25v + 25E
2. Expanding equation 2, we get: 75 = 75v - 75E
From equation 1, we can isolate v: 25v = 75 - 25E
Simplifying further: v = 3 - E
Now, let's equate this to equation 2: 3 - E = 75v - 75E
Substituting the value of v: 3 - E = 75(3 - E) - 75E
Simplifying further: 3 - E = 225 - 75E - 75E
Combining like terms: 150E = 222
Dividing both sides by 150: E = 222/150
Simplifying: E = 1.48 m/s
Therefore, the speed of the escalator is 1.48 m/s.