Strategic Problem? (May involve some algebra)

[thunderfury]

It goes something like this:

Tillie the tuna is giving her first concert. The underwater amphitheater is full and waiting for Tillie, Sharleen Shark, and the Fluke Wellington Orchestra. The concert will end with the choir of Angelfish. Molly Marlin is behind the curtain, peeking out at the audience, as Tillie begins singing. Molly notices that in the first five minutes of Tillie's performance, the entire front row of 60 fish get up, swim off, and demand their money back! Molly doesn't want to carp, but she is afraid that if this continues, the concert will flounder. To Molly's horror, 114 fish leave in the next five minutes, 90% more than the number of fish that left in the first five minutes. If this same rate of departure continues, how long will it take before all 2,200 patrons are gone?Explain in detail how you found your answer using words and numbers.

:smile:I don't know how to solve this problem, and I keep on getting decimals, but I don't know if I'm supposed to round them accordingly, or if I did something wrong. I would appreciate some help!​

 

[tkhunny]

First, you may wish to buy a salami and beat yourself over the head for 20 minutes. This may make your head feel about the same as reading through this problem. Why would anyone write such a problem? GGGGAAAaaaa...!!!!

60
60 + .9*60 = 60 + 54 = 114

Now we have a choice. The words are "same rate of departure". This may be simpler than you think. The rate of departure is 114 every 5 minutes. If that rate continues, we have (2200 - 60 - 114) / 114 = 17.7ish, so 18 more 5-minute chunks of time. We already had two such chunks of time, so that's 20 total 5-minute time periods.

You MAY be thinking the problem statement says "same rate of increase of the rate of departure". This would mean the third 5 minutes would observe the exit of one of these:

1) 60 + .9*60 + .9*.9*60 = 60 + 54 + 48.6 = 163ish
2) 114 + .9*114 = 114 + 102.6 = 217ish

I could argue either of those, I suppose, but I think the problem does NOT say that. The first exist of 60 and the 90% increase to 114 are just smoke screens. Don't be fooled by them.

My views. I welcome others'.