A jet flies from Atlanta to Dubuque a distance of 900 miles. After traveling the same amount of time on the return flight,the pilot mentioned they still had 150 miles to go. The airspeed of the plane was 300 miles per hour. How fast was the wind blowing?
speed of wind --- x mph
speed of plane --- 300 mph
speed against wind --- 300-x
speed with the wind --- 300+x
time for Atlanta to Dubuque = 900/(x+300)
coming back when time was the same --- 750/(300-x)
900/(300+x) = 750/(300-x)
270000 - 900x = 225000 + 750x
45000 = 1650x
x=300/11
x = 27.2727... mph
To find out how fast the wind was blowing, we need to use the concept of relative velocity. Let's break down the problem step-by-step:
1. Let's assume the speed of the wind is represented by 'x' miles per hour. Since we don't know the direction of the wind (whether it's with or against the plane), we'll consider it in both scenarios.
2. The total distance traveled by the jet from Atlanta to Dubuque is 900 miles. So, the total time taken in this leg of the journey is given by the distance divided by the speed:
Time = Distance / Speed
Time = 900 miles / (300 miles per hour + x miles per hour) [Since the wind may be against the plane]
3. On the return flight, the pilot mentions they have 150 miles to go. So, the total time taken in this leg of the journey can be calculated similarly:
Time = Distance / Speed
Time = 150 miles / (300 miles per hour - x miles per hour) [Since the wind may be with the plane]
4. Since the pilot spends the same amount of time on both legs of the journey, we can set the two time equations equal to each other:
900 / (300 + x) = 150 / (300 - x)
5. Now, let's solve this equation to find the value of 'x':
Cross-multiply and simplify:
(900)(300 - x) = (150)(300 + x)
270,000 - 900x = 45,000 + 150x
1,050x = 225,000
x = 225,000 / 1,050
x ≈ 214.29
Therefore, the wind was blowing at approximately 214.29 miles per hour.