A plane makes an 900-mile flight in
3 1/3 hours against a strong head wind, but returns in 50 minutes less with the wind. What is the plane's speed without the wind?
Vp-Vw=900/(10/3) = 900 * 3/10 = 270 mi/h
Vp+Vw=900/(50/60)=900 * 60/50=1080 mi/h
Vp - Vw = 270
Vp + Vw = 1080
Sum: 2Vp = 1350
Vp = 675 mi/h. = Velocity of plane without the wind.
Correction:
T = 10/3-6/5 = 50/15 - 18/15 = 32/15 =
2.1333 h
Vp+Vw = 900/2.1333 = 421.875 mi/h
Vp = (270+421.875)/2 = 346 mi/h = Velocity of the plane without wind.
To find the plane's speed without the wind, we need to use the formula:
Speed = Distance / Time
Let's break down the information given in the problem:
1. The plane makes a 900-mile flight against a strong headwind in 3 1/3 hours.
2. The plane makes its return journey in 50 minutes less time with the wind.
Step 1: Convert the time measurements to a common unit.
We need to convert 3 1/3 hours and 50 minutes to a common unit, either hours or minutes.
3 1/3 hours can be written as (3 + 1/3) hours, which is equal to (3 + 20/60) hours, or 10/3 hours.
50 minutes is equal to 50/60 hours, or 5/6 hours.
Step 2: Calculate the speed against the wind.
Using the formula, Speed = Distance / Time, we can calculate the speed against the wind.
Speed against the wind = 900 miles / (10/3 hours) = (900 miles) * (3/10) = 270 miles per hour.
Step 3: Calculate the speed with the wind.
Since the return journey takes 50 minutes less with the wind, we subtract 5/6 hours from the time it took against the wind to determine the time for the return journey.
Time with the wind = 10/3 hours - 5/6 hours = (20/6 - 5/6) hours = 15/6 hours = 2.5 hours.
Using the formula, Speed = Distance / Time, we can calculate the speed with the wind.
Speed with the wind = 900 miles / (2.5 hours) = 360 miles per hour.
Step 4: Calculate the speed without the wind.
To find the plane's speed without the wind, we need to calculate the average speed of the plane when flying against and with the wind.
Average speed = (Speed with the wind + Speed against the wind) / 2
Average speed = (360 miles per hour + 270 miles per hour) / 2 = 630 miles per hour / 2 = 315 miles per hour.
Therefore, the plane's speed without the wind is 315 miles per hour.