The hot air balloon descends at a rate of 100 feet per minute, so after 15 minutes, it would have descended:
100 feet/minute * 15 minutes = 1500 feet
The submarine ascends at a rate of 40 feet per minute, so after 15 minutes, it would have ascended:
40 feet/minute * 15 minutes = 600 feet
Now, to find the vertical distance between them, you subtract the depth of the submarine from the height of the hot air balloon:
1500 feet (balloon's descent) - 600 feet (submarine's ascent) = 900 feet
So, after 15 minutes, the vertical distance between the hot air balloon and the submarine is 900 FEET.