This is soooo confusing!
An airplane flies from New Orleans, Louisiana, to Atlanta, Georgia, at an average rate of 320 miles per hour. The airplane then returns at an average rate of 280 miles per hour. The total travel time is 3 hours.
A. Define a variable for the flying time from New Orleans to Atlanta. Write an expression for the travel time from Atlanta to New Orleans.
B. Write and solve an equation to find the flying time from New Orleans to Atlanta.
A. Let's define the flying time from New Orleans to Atlanta as 'x' hours. To find the travel time from Atlanta to New Orleans, we need to consider that the total travel time is 3 hours. So, the travel time from Atlanta to New Orleans would be the remaining time after subtracting the flying time from the total travel time.
Travel time from Atlanta to New Orleans = Total travel time - Flying time from New Orleans to Atlanta
Travel time from Atlanta to New Orleans = 3 hours - x hours
The expression for the travel time from Atlanta to New Orleans is 3 - x.
B. To write and solve an equation to find the flying time from New Orleans to Atlanta, we need to consider that the distance traveled is the same for both legs of the trip. The distance can be calculated using the formula: Distance = Speed × Time.
The distance from New Orleans to Atlanta = Speed × Flying time from New Orleans to Atlanta
The distance from Atlanta to New Orleans = Speed × Travel time from Atlanta to New Orleans
Since the distances are the same, we can set the two equations equal to each other:
Distance from New Orleans to Atlanta = Distance from Atlanta to New Orleans
Speed × Flying time from New Orleans to Atlanta = Speed × Travel time from Atlanta to New Orleans
Given that the average rate of the airplane from New Orleans to Atlanta is 320 miles per hour and from Atlanta to New Orleans is 280 miles per hour, the equation becomes:
320x = 280(3 - x)
Now, let's solve the equation to find the flying time from New Orleans to Atlanta:
320x = 280(3 - x)
320x = 840 - 280x
Combining like terms:
320x + 280x = 840
600x = 840
Dividing both sides of the equation by 600:
x = 840/600
x = 1.4
Therefore, the flying time from New Orleans to Atlanta is 1.4 hours.
You are going to use the formula
distance = rate x time
time = distance/rate
A) let the time taken for NO to A flight be t hrs
then time taken for A to NO flight is 3-t hrs
B)
320t = 280(3-t)
320t = 840 - 280t
600t = 840
t = 840/600 = 1.4