{"id":14813,"date":"2018-04-22T23:41:07","date_gmt":"2018-04-22T22:41:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14813"},"modified":"2022-01-10T00:11:22","modified_gmt":"2022-01-10T00:11:22","slug":"quando-o-jorge-se-desloca-a-lisboa","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14813","title":{"rendered":"Quando o Jorge se desloca a Lisboa"},"content":{"rendered":"<p><ul id='GTTabs_ul_14813' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14813' class='GTTabs_curr'><a  id=\"14813_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14813' ><a  id=\"14813_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_14813'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O Jorge reside numa aldeia do norte de Portugal e vai frequentemente a Lisboa.<br \/>\nQuando o Jorge se desloca \u00e0 velocidade m\u00e9dia de 80 km\/h, demora mais uma hora do que quando se desloca \u00e0 velocidade m\u00e9dia de 100 km\/h.<\/p>\n<p>Qual \u00e9 a dist\u00e2ncia, em quil\u00f3metros, que o Jorge percorre quando se desloca da sua aldeia a Lisboa?<br \/>\nMostra como chegaste \u00e0 tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14813' onClick='GTTabs_show(1,14813)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14813'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Comecemos por tabelar os dados.<\/p>\n<table class=\" aligncenter\" style=\"width: 60%;\">\n<tfoot>\n<tr>\n<td><strong>Dist\u00e2ncia percorrida na viagem<\/strong> (em km)<\/td>\n<td><strong>\\(d\\)<\/strong><\/td>\n<td><strong>\\(d\\)<\/strong><\/td>\n<\/tr>\n<\/tfoot>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">Velocidade m\u00e9dia (em km\/h) &#8211;\u00a0<strong>\\(v\\)<\/strong><\/td>\n<td>80<\/td>\n<td>100<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">Dura\u00e7\u00e3o da viagem (em horas) &#8211;\u00a0<strong>\\(t\\)<\/strong><\/td>\n<td>\\({x + 1}\\)<\/td>\n<td>\\(x\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Como as grandezas <em>v<\/em> e <em>t<\/em> s\u00e3o inversamente proporcionais, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{80 \\times \\left( {x + 1} \\right) = 100 \\times x}&amp; \\Leftrightarrow &amp;{100x &#8211; 80x = 80}\\\\{}&amp; \\Leftrightarrow &amp;{20x = 80}\\\\{}&amp; \\Leftrightarrow &amp;{x = 4}\\end{array}\\]<\/p>\n<p>Assim, a dist\u00e2ncia percorrida na viagem \u00e9\u00a0\\({80^{km\/h}} \\times {5^h} = {40^{km}}\\).<\/p>\n<p>Portanto, \u00e9 de 400 km a dist\u00e2ncia que o Jorge percorre quando se desloca da sua aldeia a Lisboa.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14813' onClick='GTTabs_show(0,14813)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Jorge reside numa aldeia do norte de Portugal e vai frequentemente a Lisboa. Quando o Jorge se desloca \u00e0 velocidade m\u00e9dia de 80 km\/h, demora mais uma hora do que&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14815,"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-14813","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":2723,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag122-7a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14813","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=14813"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14813\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14815"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14813"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14813"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14813"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14813"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}