# Hot-Air Balloon Project

## Question 1

The function for the descent of the first balloon is y=800-20x.

The variables:

y= The altitude it feet

x=Minutes

## Question 3

To find the height of the balloon 5 minutes before it was sighted, we must replace x in the function, y=800-20x, with -5. When you solve the equation, you come up with the answer of y=900 feet. So the balloon was 900 feet in the air, 5minutes before it was sighted.

## Question 4

To find the amount of time that it takes the first balloon to reach an altitude of 20 feet, we must replace y in the function,y=800-20x, with 20. When we solve the equation you come up with x=39 minutes.

## Question 5

The function for the descent of the second balloon is y=1200-20x and the second balloon will land 20 minutes after the first ballon lands. Both balloons descend at the same rate but the second one starts at a higher altitude. The lines remain apart by the same distance and will never touch.

## Question 6

The function for the descent of the third balloon is y=800-30x. The third balloon reaches the ground after 26 minutes and 40 seconds but it lands 13 minutes and 20 seconds before the first balloon.The third balloon descends at a faster rate and it reaches the ground faster. Both lines start at the same point on the y-axis but the distance between them gets larger the father they go on the x-axis.

## Question 7

The function for the ascent of the forth balloon is y=30x. To find the point where the first and the fourth balloon will be at the same altitude at the same time you have to write the equation, 800-20x=30x, and solve. Both balloons will be at the same altitude 16 minutes after the fourth balloon is launched and both balloons will be 480 feet in the air. In the graph this will be represented by the intersection of the two lines.

## Question 8

The equation for the 3rd balloon is y=800-30x and the equation for the 1st balloon is y=800-20x. To find the height that the 3rd balloon would have to start its descent so that it hits the ground at the same time as the 1st balloon you have the replace the 800 in the equation for the 3rd balloon. In the 1st equation, x has to be 40 (minutes) so that y (altitude) can be 0 (ground level). If you replace x in the 3rd equation with 40 (minutes) then, y (altitude) will be -400. To make the y=0 you would have to add 400 and since you do the same to both sides of the equation then you would add 400 to the 3rd equation to make the new equation y=1200-30x. When you replace x with 40, y becomes 0 (ground level) and both balloons land at the same time.