Answer:
The distance from the airport to the corporate offices is 110 miles.
Explanation:
Let d be the distance from the airport to the office (at a velocity of 75 mph), the person travels an entire distance of 156 miles, 156-d is the distance from home to the airport (at a velocity of 30 mph).
The equaiton for velocity is:
[tex]Velocity=\frac{distance}{time}[/tex]
From this you can find the equation for the time:
[tex]time=\frac{distance}{velocity}[/tex]
You can use the total time to find the distance d because you know that the time between the home and the airport plus the time between the airport and the work is 3 hours:
[tex]3=\frac{156-d}{30}+\frac{d}{75}[/tex]
You can solve the equation to find d:
[tex]3=\frac{156*75-75d+30d}{30*75}[/tex]
[tex]3=\frac{11700-45d}{2250}\\d=-\frac{(3*2250)-11700}{45}\\d=110[/tex]
Now you have that the distance between the airport and the office is 110 miles.
