# I have a button…(story problem)

Tom has a job. He is a button pusher. He works for 8 hours per day. his job at work is simply to push a button. He has some freedoms and some limitations. When he arrives to work each day he has 5 button pushes in his bank. Each time he pushes the button he gets a reward. He can push the button as often as he would like, until it gets to zero, then pushing the button does nothing. Every 5 minutes he gets 1 push added to his bank, however his bank cannot exceed 5 pushes. Tom wants to know if he would get more rewards total in 8 hours if he a)pressed the button 5 times as soon as he got to work and then every 5 minutes after that, or b)he paced himself, pressing it every X minutes:seconds, pressing it only often enough to never reach 0 in the bank. And what would X be?

My problem is that i cant figure out how to get to x. I am almost 30 and haven't done much math since highschool. would I be on the correct path if i first started with how many times 25 goes into 8 hours? (the 60 minutes in an hour is really throwing a curve ball at me)

Also I am new to this site, I found it on google, so I really feel welcome when I start receiving down votes from users and no reasoning why. I will look elsewhere for help next time, thanks.

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Can you share your efforts, and explain what you've tried? – user61527 Jan 18 '14 at 19:09
see here...math.stackexchange.com/questions/642842/… – ChristopherT Jan 18 '14 at 19:11
updated with what I could provide. I dont know where to start, so I have no efforts to share. – ChristopherT Jan 18 '14 at 19:34

My thought is that he would get the same number of rewards if in the second option his last button push brings his "push count" to 0.

In the first option, he gets 5 rewards instantly, then he pushes the button 5 times every 5 minutes for the next 480 minutes for a total of 485 rewards.

In the second option, he pushes the button every 59.38 seconds (96/97 seconds) until the last minute of the day when he pushed it for the 485th time and brought his count to zero.

If he still must have one left in his "push count" at the end of the day, then option one will afford him one more reward than will option two.

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Also, if he must have one left in his "push count" at the end of the day, then he will get 484 rewards.

He would push the button every 480/484 minutes. This is equal to 120/121 minutes or approximately 59.5 seconds.

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