An executive drove from home at an average speed of 45 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 120 mph. The
entire distance was 250 miles; the entire trip took three hours. Find the distance from the airport to the
corporate offices.
If the distance from the airport to the offices is x, then he drove 250-x miles.
Since time = distance/speed,
(250-x)/45 + x/120 = 3
Now just solve for x
To find the distance from the airport to the corporate offices, we need to first determine the time it took for the executive to reach the airport and the time it took for the helicopter to reach the corporate offices.
Let's assume the distance from the executive's home to the airport is "x" miles.
Since the executive traveled at an average speed of 45 mph, the time taken to travel from home to the airport would be:
Time = Distance / Speed
Time = x / 45
Now let's calculate the time taken for the helicopter to fly from the airport to the corporate offices.
Since the total distance is 250 miles and the time taken for the entire trip was 3 hours, the time taken for the helicopter to fly would be:
Time = Total Time - Time to reach the airport
Time = 3 - (x / 45)
The time taken for the helicopter to fly is also given by:
Time = Distance / Speed
Time = Distance / 120
Since we know that the time taken for the helicopter to fly is the same as the time calculated above, we can equate the two expressions for time:
Distance / 120 = 3 - (x / 45)
Now, we can solve for the distance from the airport to the corporate offices by rearranging the equation and simplifying:
Distance = (3 - (x / 45)) * 120
Distance = (360 - 8x) / 3
Therefore, the distance from the airport to the corporate offices is (360 - 8x) / 3 miles.