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.
distance by car --- x miles
distance by copper -- 250-x miles
x/45 + (250-x)/120 = 3
each term times 360 , the LCD
8x + 3(250-x) = 1080
8x - 3x = 330
x = 66
I will let you finish it
Let's assume the distance from the executive's home to the airport is x miles.
Since the executive drove at an average speed of 45 mph and the distance is x miles, it took him x/45 hours to reach the airport.
The remaining distance from the airport to the corporate offices is 250 - x miles.
Since the executive flew at an average speed of 120 mph and the remaining distance is 250 - x miles, it took him (250 - x)/120 hours to reach the corporate offices.
The total time taken for the trip is given as 3 hours.
Therefore, we can set up the equation: x/45 + (250 - x)/120 = 3.
To solve this equation, we can first eliminate the fractions by multiplying both sides of the equation by 120 * 45 = 5400.
5400 * (x/45) + 5400 * ((250 - x)/120) = 3 * 5400.
120x + 45(250 - x) = 16200.
120x + 11250 - 45x = 16200.
75x + 11250 = 16200.
75x = 49650.
x = 66.
Therefore, the distance from the airport to the corporate offices is 250 - x = 250 - 66 = 184 miles.
To find the distance from the airport to the corporate offices, we can set up a system of equations based on the given information.
Let's assume the distance from the executive's home to the airport is represented by "x" miles. Since the entire distance of the trip is 250 miles, the distance from the airport to the corporate offices would be (250 - x) miles.
Now, we can use the formula: time = distance / speed
The time taken to drive from home to the airport can be calculated as x miles / 45 mph, and the time taken to fly from the airport to the corporate offices can be calculated as (250 - x) miles / 120 mph.
Given that the entire trip took three hours, the sum of the times taken to drive and fly should equal 3 hours:
x / 45 + (250 - x) / 120 = 3
To solve for x, we can multiply the entire equation by 360, which is the least common multiple of 45 and 120:
8x + 3(250 - x) = 1080
Now, we can simplify the equation:
8x + 750 - 3x = 1080
5x + 750 = 1080
5x = 330
x = 66
So, the distance from the airport to the corporate offices would be 250 - x = 250 - 66 = 184 miles.
Therefore, the distance from the airport to the corporate offices is 184 miles.