Ahot air balloon leaves the ground and ascends at a rate of 6 feet per second for 3 minutes. then it descends at a rate of 3 feet per second for 2 minutes. finally, it ascends at a rate of 4 feet per second for 5 minutes. how far above the ground is the balloon now?

Hello First,

State 1:
A hot air balloon leaves the ground and ascends at a rate of 6 feet per second for 3 minutes.
1 minute = 60 seconds
3 minutes = 180 seconds
If it's rate of is 6 feet per second
Last of 3 minutes, it will ascend (180 seconds x 6 feet) 1080 feet.seconds. That is we can write +1080 feet.seconds

State 2:
Then it descends at a rate of 3 feet per second for 2 minutes.
2 minutes = 120 seconds
If it's rate of is 3 feet per second
Last of 3 minutes, it will descent (120 seconds x 3 feet) 360 feet.seconds that is we can write -360 feet.seconds

State 3:
It ascends at a rate of 4 feet per second for 5 minutes.
5 minutes = 300 seconds
If it's rate of is 4 feet per second
Last of 5 minutes, it will ascent (300 seconds x 4 feet) 1200 feet.seconds that is we can write +1200 feet.seconds

Last State:
+1080 feet.seconds ascent (1)
-360 feet.seconds descent (2)
+1200 feet.seconds ascent (3)

Conclusion:

(+1080 feet.seconds) + (-360 feet.seconds) + (+1200 feet.seconds) = +1920 feet.seconds

+1920 feet.seconds