Question

A hot air balloon is launched at kirby park, and it ascends at the rate of 7200 feet per hour. At the same time, a second hot air balloon is launched at newman park, and it ascends at a rate of 4,000 feet per hour. Both of the balloons stop ascending after 30 minutes. Kirby park has an altitude of 1,705 ft while newman park has an altitude of 3,940 ft. Are the balloons ever at the same height at the same time? explain

Answer 1

Find the height of both balloons and compare

So for both

altitude + (speed of ascent x time)

Answer 2

time = 1/2 or .5 since it is half an hour

Answer 3

wait, what's the altitude?

Answer 4

oh never mind.

Answer 5

Kirby park is at 1705

Newman park is at 3940

it's in the problem

Answer 6

so for kibry park, would it be 1705 x (7200 x.5) ?

Answer 7

Yes

Answer 8

which is 3600 added to 7200, correct?

Answer 9

i mean 1705*

Answer 10

1705 + 3600.

Answer 11

5305

Answer 12

Now do the same for the other balloon and check if 5305 = x

Answer 13

the height of that was is 5940 ft

Answer 14

so what do i do after finding both the heights?

Answer 15

Ok, i just drew the graphs for both of them. Sorry for the delay. They both will have a max height of 5305 and 5940 at 30 minutes.

I used slopes to determine if they will intersect.

y=7200x + 1705

and

y=4000x + 3940


They do not reach the same height within the 30 minutes. But will be at the same height after about 42 minutes.