{"id":2073,"date":"2021-03-27T08:09:55","date_gmt":"2021-03-27T12:09:55","guid":{"rendered":"https:\/\/josmfs.net\/?p=2073"},"modified":"2024-04-07T19:19:02","modified_gmt":"2024-04-07T23:19:02","slug":"wine-into-water-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/03\/27\/wine-into-water-problem\/","title":{"rendered":"Wine Into Water Problem"},"content":{"rendered":"

\"\"Here is a challenging problem from the 1874 The<\/em> Analyst<\/em>.<\/p>\n

\u201cA cask containing a<\/em> gallons of wine stands on another containing a<\/em> gallons of water; they are connected by a pipe through which, when open, the wine can escape into the lower cask at the rate of c<\/em> gallons per minute, and through a pipe in the lower cask the mixture can escape at the same rate; also, water can be let in through a pipe on the top of the upper cask at a like rate. If all the pipes be opened at the same instant, how much wine will be in the lower cask at the end of t<\/em> minutes, supposing the fluids to mingle perfectly?<\/p>\n

\u2014\u00a0 Communicated by Artemas Martin, Mathematical Editor of Schoolday <\/em>Magazine, Erie, Pennsylvania.\u201d<\/p>\n

I found the problem in Benjamin Wardhaugh\u2019s book where he describes The<\/em> Analyst<\/em>:<\/p>\n

\u201cBeginning in 1874 and continuing as Annals of Mathematics<\/em> from 1884 onward, The Analyst<\/em> appeared monthly, published in Des Moines, Iowa, and was intended as \u201ca suitable medium of communication between a large class of investigators and students in science, comprising the various grades from the students in our high schools and colleges to the college professor.\u201d It carried a range of mathematical articles, both pure and applied, and a regular series of mathematical problems of\u00a0 varying difficulty: on the whole they seem harder than those in The Ladies\u2019 Diary<\/em> and possibly easier than the Mathematical Challenges<\/em> in the extract after the next. Those given here appeared in the very first issue.\u201d<\/p>\n

I tailored my solution after the \u201cDiluted Wine Puzzle<\/a>\u201d, though this problem was more complicated.\u00a0 Moreover, the final solution must pass from discreet steps to continuous ones.<\/p>\n

There is a bonus problem in a later issue:<\/p>\n

\u201c19.\u00a0 Referring to Question 4, (No. 1): At what time will the lower cask contain the greatest quantity of wine?<\/p>\n

\u2014Communicated by Prof. Geo. R. Perkins.\u201d<\/p>\n

Answer<\/a>.<\/p>\n

See the Wine Into Water Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here is a challenging problem from the 1874 The Analyst. \u201cA cask containing a gallons of wine stands on another containing a gallons of water; they are connected by a pipe through which, when open, the wine can escape into the lower cask at the rate of c gallons per minute, and through a pipe […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[32,242,218],"class_list":["post-2073","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-calculus","tag-mixture-problems","tag-the-analyst"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2073","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2073"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2073\/revisions"}],"predecessor-version":[{"id":3695,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2073\/revisions\/3695"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2073"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2073"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}