Two hot air balloons are in flight above a field. The first Balloon is 30 meters above the ground rising 25 meters per minute. The Second Balloon is 300 meters above the ground descending 20 meters per minute.
When will the 2 balloons be at the same altitude? What would be the altitude at that time? Use mathmatics to explain and support your answer
write 2 equations
30+25m
and
300-20m
set them equal to each other and solve for m
Im sorry Im new to this how do I solve for M
30+25M = 300-20M
I got 6 when solving for M but i dont know how to explain
To find out when the two balloons will be at the same altitude, we need to set up an equation based on their respective altitudes. Let's assume that after "t" minutes, the first balloon will have reached an altitude of h1 and the second balloon will have reached an altitude of h2.
For the first balloon:
h1 = 30 + 25t
For the second balloon:
h2 = 300 - 20t
To find the time when the two balloons are at the same altitude, we can set h1 equal to h2 and solve for "t":
30 + 25t = 300 - 20t
Combining like terms:
45t = 270
Dividing both sides by 45:
t = 6
Therefore, after 6 minutes, the two balloons will be at the same altitude. To find the altitude at that time, we substitute the value of t into either h1 or h2:
For the first balloon:
h1 = 30 + 25t
h1 = 30 + 25(6)
h1 = 30 + 150
h1 = 180
For the second balloon:
h2 = 300 - 20t
h2 = 300 - 20(6)
h2 = 300 - 120
h2 = 180
So, after 6 minutes, both balloons will be at an altitude of 180 meters.