John and Max and climbing a 45 foot tree together to reach the observation area at foot 30. In 30 seconds, they manage to climb 3 feet. However, right after these 30 seconds, Max pulls John down 2 feet. When do they first reach the observation area?
I found a different answer than my friend and got 14 minutes. He got 15. Can I get some clarification about which answer is correct?
You are correct.
In $27$ intervals (each of $30$ second duration), the climbers have ascended $27$ feet (net $3-2 = 1$ foot each interval).
In the next interval, the observation post has been reached because $27 + 3 = 30$ (at this point, the pulling back down doesn't matter). So that's $28$ intervals, or $14$ minutes.
This is a common theme for simple puzzles. Another variation is the frog that climbs up and slips down a fixed distance each way while going up a well.
In 30 seconds climbed up 3 feet and pulled back 2 feet.
So after 30 seconds at 1 feet.
After 1 minute at 2 feet.
So after 12 minutes at 2 × 12 = 24 feet.
In next 30 seconds = 24 + 3 - 2 = 25 feet
Again next 30 seconds = 25 + 3 - 2 = 26 feet
Again next 30 seconds = 26 + 3 - 2 = 27 feet.
In next 30 seconds = 27 + 3 = 30 feet.
As he reached and can't be pulled back.
Total time = 12 minutes + 4 × 30 seconds
= 12 minutes + 4 minutes = 16 minutes.