A plane traveling from Phoenix to Washington, D.C with a tailwind of 20 miles per hour takes 3 hours. The return trip in the same wind, which is now a headwind, takes the same plane 3 hours and 12 minutes. What is the average speed of the plane in calm conditions?
600 miles/hour
620 miles/hour
650 miles/hour
700 miles/hour
620 miles/hour
3(s+20) = 3.20(s-20)
s = 620
3*640 = 1920
3840/(3 + 3.20) = 619.35
so you are correct
To find the average speed of the plane in calm conditions, we need to consider the formula:
Average speed = Total distance / Total time.
Let's calculate the total distance for both trips first:
For the trip from Phoenix to Washington, D.C:
Speed of the plane with the tailwind is plane's ground speed + tailwind speed = x + 20 mph.
The time taken for this trip is 3 hours.
So, the total distance covered is (x + 20) mph * 3 hours.
For the return trip from Washington, D.C to Phoenix:
Speed of the plane with the headwind is plane's ground speed - headwind speed = x - 20 mph.
The time taken for this trip is 3 hours + 12 minutes = 3.2 hours.
So, the total distance covered is (x - 20) mph * 3.2 hours.
Since the total distance covered in both trips is the same, we can equate the two expressions:
(x + 20) mph * 3 hours = (x - 20) mph * 3.2 hours.
Simplifying this equation:
3(x + 20) = 3.2(x - 20).
Distributing and simplifying further:
3x + 60 = 3.2x - 64.
Subtracting 3x and adding 64 on both sides:
60 + 64 = 3.2x - 3x.
Simplifying:
124 = 0.2x.
Dividing both sides by 0.2:
x = 124 / 0.2.
Calculating x:
x = 620 miles/hour.
Therefore, the average speed of the plane in calm conditions is 620 miles/hour.
Hence, the correct answer is 620 miles/hour.
To find the average speed of the plane in calm conditions, we can use the formula: average speed = total distance / total time.
First, let's find the total distance of one leg of the trip. Since the plane took 3 hours to travel from Phoenix to Washington, D.C with a tailwind of 20 mph, the distance would be:
Distance = speed * time
Distance = (plane's speed + tailwind speed) * time
Distance = (x mph + 20 mph) * 3 hours
Distance = (x + 20) * 3
Now, let's find the total distance of the return trip. Since the plane took 3 hours and 12 minutes (which is 3 + 12/60 = 3.2 hours) to travel from Washington, D.C to Phoenix with a headwind of 20 mph, the distance would be:
Distance = speed * time
Distance = (plane's speed - headwind speed) * time
Distance = (x mph - 20 mph) * 3.2 hours
Distance = (x - 20) * 3.2
Since the total distance on the outbound trip is the same as the total distance on the return trip, we can set up an equation:
(x + 20) * 3 = (x - 20) * 3.2
Now, let's solve for x:
3x + 60 = 3.2x - 64
0.2x = 124
x = 620
Therefore, the average speed of the plane in calm conditions is 620 miles/hour. So the correct answer is option B: 620 miles/hour.