Question

You are part of the rescue team in a ship at sea. One of your divers is 250 feet below sea level, and she injured herself. She has only a 7 minute supply of air in her tank, and can only rise towards the surface at a rate of 10 feet per minute. You are sending down a rescue sub. The sub can descend at a rate of 30 feet per minute. At what depth, to the nearest foot, will the two meet?

Answer 1

To determine at what depth the rescue sub will meet the injured diver, we need to first calculate how long it will take the diver to reach the surface. Because the diver is rising at a rate of 10 feet per minute, and she has a 7 minute supply of air, it will take her 7 minutes to reach the surface.

Next, we need to calculate how long it will take the rescue sub to reach the diver. Because the diver is 250 feet below the surface, and the sub is descending at a rate of 30 feet per minute, it will take the sub 250 feet / 30 feet/minute = <<250/30=8.33>>8.33 minutes to reach the diver.

Finally, to determine at what depth the two will meet, we need to subtract the time it takes the diver to reach the surface (7 minutes) from the time it takes the sub to reach the diver (8.33 minutes). This gives us a total time of 8.33 minutes - 7 minutes = 1.33 minutes.

Since the diver is rising at a rate of 10 feet per minute, and the total time is 1.33 minutes, the depth at which the two will meet is 1.33 minutes * 10 feet/minute = 13.3 feet. Rounding to the nearest foot, we get a depth of 13 feet. Therefore, the rescue sub and the diver will meet at a depth of approximately 13 feet.