SOLUTION: Solve the following problem from Pacioli – A mouse is at the top of a poplar tree that is 60 feet high, and a cat is on the ground at its foot. The mouse descends 1⁄2 of a fo

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Solve the following problem from Pacioli – A mouse is at the top of a poplar tree that is 60 feet high, and a cat is on the ground at its foot. The mouse descends 1⁄2 of a fo      Log On

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Question 1126924: Solve the following problem from Pacioli – A mouse is at the top of a poplar tree that is 60 feet high, and a cat is on the ground at its foot. The mouse descends 1⁄2 of a foot each day, and at night it turns back 1/6 of a foot. The cat climbs 1 foot a day and slips back 1⁄4 of a foot each night. The tree grows 1⁄4 of a foot between the cat and the mouse each day and shrinks 1/8 of a foot each night. How long will it take the cat to reach the mouse?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = number of [1 day + 1 night] intervals
The mouse's rate of descent is +%281%2F3%29%2F1+
The cat's rate of ascent is +%283%2F4%29%2F1+
I can add their rates since they are going toward each other
Subtract the rate of growth of the tree +%281%2F8%29%2F1+
------------------------
+%281%2F3%29%2At+%2B+%283%2F4%29%2At+-+%281%2F8%29%2At+=+60+
Multiply both sides by +48+
+16t+%2B+36t+-+6t+=+2880+
+46t+=+2880+
+t+=+62.6087+
I would say it takes 31 days and 32 nights
get another opinion definitely