Two hot air ballons are in flight above a field. The first balloon is 30 meters above ground and rising 25 meters per minute. The second ballon is 300 meters above ground and descending 20 meters per minute. When will the two balloons be at the same altitude? and what would be the altitude at that time?
after t minutes, you want
30+25t = 300-20t
30=25t=300-20t
To find out when the two balloons will be at the same altitude, we need to set up an equation based on the rate of change of their altitudes.
Let's assume the time at which the two balloons will be at the same altitude is 't' minutes.
For the first balloon, the altitude at time 't' can be determined using the equation:
Altitude of the first balloon = 30 + 25t
Similarly, for the second balloon, the altitude at time 't' can be determined using the equation:
Altitude of the second balloon = 300 - 20t
To find when the two balloons will be at the same altitude, we'll set the two equations equal to each other and solve for 't':
30 + 25t = 300 - 20t
Adding 20t to both sides:
30 + 25t + 20t = 300 - 20t + 20t
45t = 300
Dividing by 45:
t = 300 / 45
t = 6.67 (rounded to two decimal places)
Therefore, the two balloons will be at the same altitude approximately 6.67 minutes after the observation started.
To find the altitude of the balloons at that time, we can substitute the value of 't' back into either of the equations. Let's use the equation for the first balloon:
Altitude of the first balloon = 30 + 25t
Altitude of the first balloon = 30 + 25 * 6.67
Altitude of the first balloon = 30 + 166.75
Altitude of the first balloon = 196.75 meters
So, at approximately 6.67 minutes, both balloons will be at an altitude of 196.75 meters.