{"id":14859,"date":"2018-04-24T23:45:47","date_gmt":"2018-04-24T22:45:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14859"},"modified":"2022-01-10T01:04:12","modified_gmt":"2022-01-10T01:04:12","slug":"tres-torneiras-enchem-um-tanque-com-agua","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14859","title":{"rendered":"Tr\u00eas torneiras enchem um tanque com \u00e1gua"},"content":{"rendered":"<p><ul id='GTTabs_ul_14859' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14859' class='GTTabs_curr'><a  id=\"14859_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14859' ><a  id=\"14859_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14859'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Tr\u00eas torneiras id\u00eanticas, abertas completamente, enchem um tanque com \u00e1gua em 2 h 25 min.<br \/>\nSe, em vez de tr\u00eas, fossem cinco torneiras, quanto tempo levar\u00edamos para encher o mesmo tanque?<\/p>\n<p>Explica a tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14859' onClick='GTTabs_show(1,14859)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14859'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Seja <em>x<\/em> o caudal de cada uma dessas torneiras, em m<sup>3<\/sup>\/h, abertas completamente.<\/p>\n<p>Ora,\u00a0\\({2^h}\\;{25^{\\min }} = {\\left( {\\frac{{145}}{{60}}} \\right)^h} = {\\left( {\\frac{{29}}{{12}}} \\right)^h}\\).<\/p>\n<table class=\" aligncenter\" style=\"width: 60%;\">\n<tbody>\n<tr>\n<td>N\u00famero de torneiras iguais<\/td>\n<td>3<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">Caudal do conjunto de torneiras (em m<sup>3<\/sup>\/h) &#8211;\u00a0\\(c\\)<\/td>\n<td>\\(3x\\)<\/td>\n<td>\\(5x\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">Tempo de enchimento do tanque (em horas) &#8211;\u00a0\\(t\\)<\/td>\n<td>\\({\\frac{{29}}{{12}}}\\)<\/td>\n<td>\u00a0\\(t&#8217;\\)<\/td>\n<\/tr>\n<tr>\n<td>Capacidade do tanque (em m<sup>3<\/sup>)<\/td>\n<td>\u00a0\\(\\frac{{29x}}{4}\\)<\/td>\n<td>\u00a0\\(\\frac{{29x}}{4}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Como as grandezas <em>c<\/em> e <em>t<\/em> s\u00e3o inversamente proporcionais, ent\u00e3o \u00e9 constante o produto das medidas correspondentes dessas grandezas. Por isso, temos:\\[\\begin{array}{*{20}{l}}{3x \\times \\frac{{29}}{{12}} = 5x \\times t&#8217;}&amp; \\Leftrightarrow &amp;{3 \\times \\frac{{29}}{{12}} = 5 \\times t&#8217;}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{{29}}{4} = 5 \\times t&#8217;}\\\\{}&amp; \\Leftrightarrow &amp;{t&#8217; = \\frac{{29}}{{20}}}\\end{array}\\]<\/p>\n<p>Ora,\u00a0\\({\\left( {\\frac{{29}}{{20}}} \\right)^h} = {\\left( {\\frac{{87}}{{60}}} \\right)^h} = {\\left( {1 + \\frac{{27}}{{60}}} \\right)^h} = {1^h}\\;{27^{\\min }}\\).<\/p>\n<p>Portanto, se fossem cinco torneiras, levar\u00edamos 1 hora e 27 minutos a encher o tanque.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14859' onClick='GTTabs_show(0,14859)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Tr\u00eas torneiras id\u00eanticas, abertas completamente, enchem um tanque com \u00e1gua em 2 h 25 min. Se, em vez de tr\u00eas, fossem cinco torneiras, quanto tempo levar\u00edamos para encher o mesmo tanque?&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14860,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,250],"series":[],"class_list":["post-14859","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-proporcionalidade-inversa-2"],"views":3183,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag125-4a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14859","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14859"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14859\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14860"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14859"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14859"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14859"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14859"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}