To determine how many miles the plane would fly in 3 hours and 15 minutes, given its speed and the tailwind, let's proceed step-by-step:
1. Determine the speed of the plane with the tailwind:
- The plane's speed is 270 miles per hour (mph).
- The tailwind speed is 30 miles per hour (mph).
Since the tailwind assists the plane's movement, the effective speed of the plane is the sum of its own speed and the tailwind speed:
[tex]\[
\text{Total Speed} = \text{Plane Speed} + \text{Tailwind Speed} = 270 \text{ mph} + 30 \text{ mph} = 300 \text{ mph}
\][/tex]
2. Convert the travel time into hours:
- The travel time is given as 3 hours and 15 minutes.
To convert the 15 minutes into hours, we use the fact that there are 60 minutes in an hour:
[tex]\[
15 \text{ minutes} = \frac{15}{60} \text{ hours} = 0.25 \text{ hours}
\][/tex]
Adding this to the 3 hours:
[tex]\[
\text{Total Time} = 3 \text{ hours} + 0.25 \text{ hours} = 3.25 \text{ hours}
\][/tex]
3. Calculate the distance traveled:
The distance a plane travels can be calculated using the formula:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
Given the total speed (300 mph) and the total time (3.25 hours), we can find the distance:
[tex]\[
\text{Distance} = 300 \text{ mph} \times 3.25 \text{ hours} = 975 \text{ miles}
\][/tex]
Therefore, the plane would fly a total of 975 miles in 3 hours and 15 minutes with a 30 mph tailwind.
