Question

An executive drove from home at an average speed of 40 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 80 mph. The entire distance was 280 mi. The entire trip took 4 h. Find the distance from the airport to the corporate offices.

Answer 1

240 miles

Explanation:

Let x = hour by car

y = hour by helicopter

The time in both the car and helicopter have to add up to equal the total time of 4 hours

x + y = 4

Since the car went 40 miles for every hour, multiply x by 40 like this: 40x

Since the helicopter went 80 miles for every hour, multiply y by 80 like this: 80y

Both of these have to sum up to 280

40x + 80y = 280

Since we're just trying to find out how long the helicopter ride was, let's get rid of the x variable by substitution method

Subtract y from both sides in the top equation

x + y = 4

- y = y

x = 4 - y

Substitute the x into the bottom equation

40(4 - y) + 80y = 280

160 - 40y + 80y = 280

160 + 40y = 280

Subtract 160 from both sides

160 + 40y = 280

- 160 - 160

40y = 120

Divide both sides by 40

40y/40 = 120/40

y = 3

This means part of the trip took 3 hours by helicopter

Since the helicopter traveled 80 mph, multiply 80 by 3 to get the total distance

80 x 3 = 240