As you hurry to catch your flight at the airport, you encounter a moving walkway that is 85m long and has a speed of 2.2 m/s relative to the ground. If it takes you 68s to cover 85m when walking on the ground, how long will it take you to cover the same distance on the walkway? Assume that you walk with the same speed on the walkway as you do on the ground.

V = 85m / 68s. = 1.25m/s Walking on ground.

t = d / V = 85m / (2.2+1.25)m/s = 24.6s.

Well, who needs a treadmill at the gym when you have a moving walkway at the airport, right? Let's do some math magic to find out how long it'll take you to cover that distance on the walkway.

When you're walking on the ground, without the assistance of the walkway, you cover 85m in 68 seconds. So, we know your speed on the ground is 85m/68s = 1.25 m/s.

Now, when you hop on the moving walkway, you become a speed demon! The walkway has a speed of 2.2 m/s relative to the ground, and you walk with the same speed on the walkway as you do on the ground. So, logically, your effective speed on the walkway is the sum of your walking speed and the walkway speed, which gives us 1.25 m/s + 2.2 m/s = 3.45 m/s.

To calculate the time it'll take you to cover the same 85m distance on the walkway, we use the formula: Time = Distance / Speed. Plugging in the values, we get Time = 85m / 3.45 m/s ≈ 24.64 seconds.

So, my friend, it'll take you approximately 24.64 seconds to cover the 85m distance on the walkway. Just don't let those groovy moving sidewalks make you trip over your own fancy footwork!

To find out how long it will take to cover the same distance on the walkway, we need to determine the effective speed at which you are moving on the walkway.

The effective speed is the sum of your walking speed on the ground and the speed of the walkway.

Given:
Length of the walkway (L) = 85m
Speed of the walkway (v) = 2.2 m/s
Time taken to cover the same distance on the ground (t_ground) = 68s

Let's calculate the effective speed on the walkway (v_effective):

v_effective = v + walking speed on the ground

Since the walking speed on the ground is not given, let's assume it as v_ground.

Now, we can use the formula for speed:

Speed = Distance / Time

we can rearrange the formula to solve for time:

Time = Distance / Speed

On the ground:
t_ground = 85m / v_ground

On the walkway:
t_walkway = 85m / v_effective

We need to find the value of t_walkway.

To calculate v_effective, we know that:

v_effective = v + v_ground

Given that t_ground = 68s, we can rearrange the formula for t_ground to solve for v_ground:

v_ground = 85m / t_ground

Now we can substitute this value into the expression for v_effective:

v_effective = v + (85m / t_ground)

Finally, substitute the given values into the equation for t_walkway:

t_walkway = 85m / (v + (85m / t_ground))

Now we can plug in the values to calculate t_walkway.

To find out how long it will take you to cover the same distance on the walkway, we need to consider the additional speed provided by the walkway.

Let's break down the problem step by step:

Step 1: Find your walking speed.
The problem states that it takes you 68 seconds to cover 85 meters when walking on the ground. To calculate your walking speed, divide the distance by the time:
Walking speed = distance / time = 85m / 68s

Step 2: Calculate the net speed on the walkway.
Since the walkway has a speed of 2.2 m/s relative to the ground, your net speed on the walkway will be the sum of your walking speed and the walkway speed:
Net speed on walkway = Walking speed + Walkway speed

Step 3: Calculate the time taken to cover the distance on the walkway.
Now that we have your net speed on the walkway, we can calculate the time it will take to cover the same distance by dividing the distance by the net speed:
Time on walkway = distance / net speed on walkway

Let's calculate the values:

Step 1: Walking speed:
Walking speed = 85m / 68s = 1.25 m/s

Step 2: Net speed on the walkway:
Net speed on walkway = Walking speed + Walkway speed
Net speed on walkway = 1.25 m/s + 2.2 m/s = 3.45 m/s

Step 3: Time taken to cover the distance on the walkway:
Time on walkway = distance / net speed on walkway
Time on walkway = 85m / 3.45 m/s

By plugging in these values into a calculator or performing the calculation manually, we find:
Time on walkway ≈ 24.64 seconds

Therefore, it will take you approximately 24.64 seconds to cover the same distance on the walkway.

b) How long would it take you to cover the 85 m length of the wolkway if once you get on the wolkway. you immediately turn around and started walking in the opposre direction with a speed of 1.3 m/s relative to the walkway?