Sure, let's solve this step by step.
### Step-by-Step Solution:
Step 1: Determine the Effective Speed of the Plane
- The speed of the plane in still air is 270 kilometers per hour (km/h).
- The speed of the tailwind aiding the plane is 30 kilometers per hour (km/h).
- To find the effective speed of the plane, we add the plane's speed and the tailwind's speed:
[tex]\[
\text{Effective speed} = 270 \text{ km/h} + 30 \text{ km/h} = 300 \text{ km/h}
\][/tex]
Step 2: Convert the Time to Hours
- The plane travels for 3 hours and 15 minutes.
- To use this time in our calculations, we need to convert the entire time to hours.
- There are 60 minutes in one hour, so 15 minutes is:
[tex]\[
\frac{15}{60} = 0.25 \text{ hours}
\][/tex]
- Adding this to the 3 hours gives us:
[tex]\[
\text{Total time in hours} = 3 + 0.25 = 3.25 \text{ hours}
\][/tex]
Step 3: Calculate the Distance Covered
- The distance traveled (in miles) is given by multiplying the effective speed by the total time.
[tex]\[
\text{Distance} = \text{Effective speed} \times \text{Total time}
\][/tex]
- Plugging in the values we have:
[tex]\[
\text{Distance} = 300 \text{ km/h} \times 3.25 \text{ hours} = 975 \text{ kilometers}
\][/tex]
Therefore, the plane would fly 975 kilometers in 3 hours and 15 minutes considering the 30 km/h tailwind.
