Two children who are bored while waiting for their flight at the airport decide to race from one end of the 20 -long moving sidewalk to the other and back. Phillippe runs on the sidewalk at 2.0 (relative to the sidewalk). Renee runs on the floor at 2.0 . The sidewalk moves at 1.5 relative to the floor. Both make the turn instantly with no loss of speed.
Who wins the race?
By how much time does the winner win?
To determine the winner of the race and the time difference, let's calculate the time it takes for each child to complete the race.
The distance the children need to cover is the length of the moving sidewalk, which is 20 units.
First, let's calculate the time it takes for Phillippe to complete the race:
Since Phillippe runs on the moving sidewalk, his effective speed will be the combination of his running speed and the speed of the moving sidewalk: 2.0 + 1.5 = 3.5 units per time.
The time it takes for Phillippe to cover the distance of 20 units at a speed of 3.5 units per time is:
Time = Distance / Speed
Time = 20 / 3.5 = 5.71 units of time.
Now let's calculate the time it takes for Renee to complete the race:
Since Renee runs on the floor without the assistance of the moving sidewalk, her speed remains constant at 2.0 units per time.
The time it takes for Renee to cover the distance of 20 units at a speed of 2.0 units per time is:
Time = Distance / Speed
Time = 20 / 2.0 = 10 units of time.
Therefore, Phillippe wins the race as he completes it in 5.71 units of time, while Renee takes 10 units of time. The winning margin is approximately 4.29 units of time.
To determine who wins the race and by how much time, we need to calculate the time it takes for each child to complete the race.
Let's start by calculating the time it takes for Philippe to complete the race:
The length of the moving sidewalk is 20 units, and Philippe runs on the sidewalk at a speed of 2.0 units relative to the sidewalk. Since the sidewalk is moving at a speed of 1.5 units relative to the floor, Philippe's speed relative to the floor can be calculated by adding the speeds:
Relative speed of Philippe = Speed of Philippe on sidewalk + Speed of sidewalk
Relative speed of Philippe = 2.0 + 1.5 = 3.5 units (relative to the floor)
Now, we can calculate the time it takes for Philippe to complete the race by dividing the distance by the relative speed:
Time taken by Philippe = Distance / Relative speed of Philippe
Time taken by Philippe = 20 / 3.5 = 5.71 units of time (approximately)
Next, let's calculate the time it takes for Renee to complete the race:
Renee runs on the floor at a speed of 2.0 units. Since she is not using the moving sidewalk, her speed remains the same throughout the race.
The distance Renee needs to cover is still 20 units.
Time taken by Renee = Distance / Speed of Renee
Time taken by Renee = 20 / 2.0 = 10 units of time
Comparing the times taken by both children, we can see that Philippe completes the race in 5.71 units of time, while Renee completes it in 10 units of time.
Therefore, Philippe wins the race.
The difference in time between the winner (Philippe) and the runner-up (Renee) is:
Time difference = Time taken by Renee - Time taken by Philippe
Time difference = 10 - 5.71 = 4.29 units of time (approximately)
So, Philippe wins the race by approximately 4.29 units of time.
Phillipe:
t(Phil)= t1+t1 =s/(v+u) + s/(v-u)= 20/(2+1.5)+20/(2-1.5) = 5.7 +40 =45.7 s
Renee:
t(Ren)=2s/v=40/2=20 s
t(Phil)- t(Ren=45.7-20=25.7 s