At the airport, Person A and Person B are walking at the same speed to catch their flight, but Person B decides to step onto the moving sidewalk, while Person A continues to walk on the stationary sidewalk. If the sidewalk moves at 1 meter per second, and it takes Person B 40
seconds less to walk the 480
-meter
distance, at what speed are Person A and Person B walking?
If A's speed is a, then B's speed is a+1
since time = distance/speed,
480/(a+1) = 480/a - 40
a = 3 m/s
Let's assume the speed at which Person A and Person B are walking is "x" meters per second.
Since Person B takes 40 seconds less to walk the 480-meter distance, we can set up the following equation to determine the time it takes for Person A and Person B to walk the same distance:
480 / x = 480 / (x + 1)
This equation is based on the fact that Person A walks the full distance at a speed of "x" meters per second, while Person B walks the distance on both the stationary sidewalk and the moving sidewalk, at a combined speed of "x + 1" meters per second.
To solve this equation, we can cross multiply:
480 * (x + 1) = 480 * x
Distributing,
480x + 480 = 480x
Simplifying,
480 = 0
The equation 480 = 0 is not possible, which means there is no solution.
Therefore, there is no speed at which Person A and Person B are walking that satisfies the given conditions.
To find the speed at which Person A and Person B are walking, we can set up a system of equations.
Let's let the speed at which Person A is walking be denoted as x (in m/s) and the speed at which Person B is walking as y (in m/s).
Person A is walking on the stationary sidewalk, so their speed is equal to x m/s.
Person B is walking on the moving sidewalk, which has a speed of 1 m/s. Therefore, the effective speed at which Person B is walking is (y + 1) m/s.
We are given two pieces of information:
1. Person B takes 40 seconds less than Person A to walk the 480-meter distance.
2. The time taken by both Person A and Person B is the same.
Using the formula time = distance / speed, we can set up the following equations:
Time taken by Person A = Distance / Speed of A
Time taken by Person B = Distance / Effective Speed of B = Distance / (y + 1)
Equation 1: 480 / x = 480 / (y + 1) + 40 (Person B takes 40 seconds less)
Equation 2: 480 / x = 480 / (y + 1) (Both take the same time)
Now, let's simplify and solve this system of equations.
First, we'll remove the fractions by cross-multiplying Equation 1:
480(x + 1) = 480x + 40(y + 1)
Simplifying, we get:
480x + 480 = 480x + 40y + 40
Next, we'll simplify Equation 2 by cross-multiplying:
480x = 480(y + 1)
Simplifying, we get:
480x = 480y + 480
Now, we can simplify further:
480x + 480 = 480y + 480 + 40y + 40
Combining like terms, we get:
480x + 480 = 520y + 520
Subtracting 480 from both sides, we have:
480x = 520y + 40
Finally, rearranging the equation, we get:
480x - 520y = 40
Now, we can solve this linear equation for the value of x and y to determine the speeds at which Person A and Person B are walking.