To find the time it takes to fly from Dallas to Boston at different speeds, we can use the concept of inverse variation. The relationship can be expressed with the formula:
\[ T = \frac{k}{S} \]
where \( T \) is the time, \( S \) is the speed, and \( k \) is a constant.
First, we need to find \( k \) using the data provided for the first flight:
- Time \( T = 4.75 \) hours
- Speed \( S = 427 \) mi/h
Substituting the known values into the equation, we get:
\[ 4.75 = \frac{k}{427} \]
To solve for \( k \), multiply both sides by 427:
\[ k = 4.75 \times 427 \]
Calculating this gives:
\[ k = 2022.25 \]
Now we can find the time it would take at the new speed of 775 mi/h:
\[ T = \frac{k}{S} = \frac{2022.25}{775} \]
Now calculate this:
\[ T = \frac{2022.25}{775} \approx 2.60516 \]
Rounding to the nearest hundredth, we get:
\[ T \approx 2.61 \text{ hours} \]
Among the provided options, the closest one is 2.62 hours.