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.

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

first distance --- x miles

distance by helicopter -- 156-x

x/30 + (156-x)/75 = 3
times 150
5x + 2(156-x) = 450
5x + 312 - 2x = 450
3x = 138
x = 46

distance from airport to office = 156-46 = 110

check:
46/30 + 110/75 = 3

Answer 2

To find the distance from the airport to the corporate offices, let's use the equation:

Distance = Speed x Time

Let's break down the information we have:

1. The executive drove from home to the airport at an average speed of 30 mph.
2. The executive flew from the airport to the corporate offices at an average speed of 75 mph.
3. The entire distance traveled from home to the corporate offices is 156 miles.
4. The total time taken for the entire trip is 3 hours.

Let's denote the distance from the airport to the corporate offices as "x" miles.

1. The distance from home to the airport can be calculated as: (30 mph) x (time taken to drive from home to the airport).

2. The distance from the airport to the corporate offices can be calculated as: (75 mph) x (time taken to fly from the airport to the corporate offices).

Now, let's calculate the time taken for each leg of the journey:

1. Time taken to drive from home to the airport = Distance / Speed = (156 - x) / 30.

2. Time taken to fly from the airport to the corporate offices = Distance / Speed = x / 75.

The total time taken for the trip is given as 3 hours:

3. Time taken to drive + Time taken to fly = Total time taken
(156 - x) / 30 + x / 75 = 3

Now, let's simplify and solve this equation to find the value of "x":

[(156 - x) / 30] + (x / 75) = 3
[(5 * (156 - x)) / 150] + (2 * x / 150) = 3
[780 - 5x + 2x] / 150 = 3
(780 - 3x) / 150 = 3
780 - 3x = 450
-3x = 450 - 780
-3x = -330
x = -330 / -3
x = 110

Therefore, the distance from the airport to the corporate offices is 110 miles.