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.
x/45+(250-x)/120=3
To find the distance from the airport to the corporate offices, we can use the concept of relative speed.
Let's assume the distance from the executive's home to the airport is "x" miles. Therefore, the distance from the airport to the corporate offices will be "250 - x" miles.
The time taken to travel from the executive's home to the airport can be calculated using the formula:
Time = Distance / Speed
So, the time taken to travel from home to the airport is: x / 45 hours.
The time taken to travel from the airport to the corporate offices can be calculated using the formula:
Time = Distance / Speed
So, the time taken to travel from the airport to the corporate offices is: (250 - x) / 120 hours.
According to the problem, the total time taken for the entire trip is 3 hours.
So the equation becomes:
x / 45 + (250 - x) / 120 = 3
To solve this equation, we can cross-multiply and rearrange the terms:
120x + 45(250 - x) = 3 * 45 * 120
Simplifying the equation gives:
120x + 11250 - 45x = 16200
Combining like terms:
75x + 11250 = 16200
Now, subtract 11250 from both sides of the equation:
75x = 16200 - 11250
Simplifying further:
75x = 4950
Dividing both sides by 75:
x = 4950 / 75
Calculating the value of x:
x = 66
Therefore, the distance from the airport to the corporate offices is 250 - x = 250 - 66 = 184 miles.