An airplane flies from New Orleans to Atlanta at a rate of 320mph. The airplane then returns at a rate of 280mph. The total travel time is 3 hours. What is the flying time from New Orleans to Atlanta?
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Paul's answer in that reply makes no sense.
To find the flying time from New Orleans to Atlanta, we can use the formula:
Time = Distance / Speed
Let's assume the distance between New Orleans and Atlanta is "D" miles.
The airplane flies from New Orleans to Atlanta at a rate of 320mph. So, the flying time for this leg of the journey can be calculated as:
Flying Time (New Orleans to Atlanta) = D / 320
The airplane then returns from Atlanta to New Orleans at a rate of 280mph. So, the flying time for this leg of the journey can be calculated as:
Flying Time (Atlanta to New Orleans) = D / 280
The total travel time is given as 3 hours. Hence, the equation becomes:
Flying Time (New Orleans to Atlanta) + Flying Time (Atlanta to New Orleans) = 3
Substituting the earlier equations, we get:
D / 320 + D / 280 = 3
To solve this equation, we can multiply both sides by 320 * 280:
280D + 320D = 3 * 320 * 280
600D = 3 * 320 * 280
Dividing both sides by 600:
D = (3 * 320 * 280) / 600
Simplifying:
D = 448 miles
Now, we can substitute this value of D back into the earlier equation to find the flying time from New Orleans to Atlanta:
Flying Time (New Orleans to Atlanta) = D / 320 = 448 / 320 = 1.4 hours or 1 hour 24 minutes
Therefore, the flying time from New Orleans to Atlanta is 1 hour and 24 minutes.
To find the flying time from New Orleans to Atlanta, we can use the concept of average speed. Average speed is defined as total distance divided by total time. We can represent the distance from New Orleans to Atlanta as 'd' and the flying time from New Orleans to Atlanta as 't' hours.
Given that the airplane flies from New Orleans to Atlanta at a rate of 320 mph, the distance traveled would be 320t. Similarly, on the return journey, the airplane flies at a rate of 280 mph, so the distance traveled would be 280(3-t) since the total travel time is 3 hours.
Now, let's set up an equation using the average speed formula:
Average speed = Total distance / Total time
Since the average speed remains constant, we have:
320 = (320t + 280(3-t)) / 3
Now, let's solve for 't':
Multiply both sides of the equation by 3:
960 = 320t + 840 - 280t
Combine like terms:
960 = 40t + 840
Subtract 840 from both sides:
120 = 40t
Divide both sides by 40:
t = 3
Therefore, the flying time from New Orleans to Atlanta is 3 hours.