Question

An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 75 mph. The entire distance was 156 mi. The entire trip took 3 h. Find the distance from the airport to the corporate offices.

Answer 1

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:

$Velocity=\frac{distance}{time}$

From this you can find the equation for the time:

$time=\frac{distance}{velocity}$

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:

$3=\frac{156-d}{30}+\frac{d}{75}$

You can solve the equation to find d:  

$3=\frac{156*75-75d+30d}{30*75}$

$3=\frac{11700-45d}{2250}\\d=-\frac{(3*2250)-11700}{45}\\d=110$

Now you have that the distance between the airport and the office is 110 miles.