{"id":14604,"date":"2018-04-17T17:36:54","date_gmt":"2018-04-17T16:36:54","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14604"},"modified":"2022-01-09T22:00:43","modified_gmt":"2022-01-09T22:00:43","slug":"um-percurso-de-comboio","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14604","title":{"rendered":"Um percurso de comboio"},"content":{"rendered":"<p><ul id='GTTabs_ul_14604' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14604' class='GTTabs_curr'><a  id=\"14604_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14604' ><a  id=\"14604_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_14604'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14605\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14605\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png\" data-orig-size=\"860,500\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Comboio\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png\" class=\"alignright size-medium wp-image-14605\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6-300x174.png\" alt=\"\" width=\"300\" height=\"174\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6-300x174.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6-768x447.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png 860w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Um comboio que anda \u00e0 velocidade m\u00e9dia de 75 km\/h faz um certo percurso em 36 minutos.<\/p>\n<p>Quanto tempo demoraria a fazer o mesmo percurso se andasse a uma velocidade m\u00e9dia de 45 km\/h?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14604' onClick='GTTabs_show(1,14604)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14604'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14605\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14605\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png\" data-orig-size=\"860,500\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Comboio\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png\" class=\"alignright size-medium wp-image-14605\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6-300x174.png\" alt=\"\" width=\"300\" height=\"174\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6-300x174.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6-768x447.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6.png 860w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Um comboio que anda \u00e0 velocidade m\u00e9dia de 75 km\/h faz um certo percurso em 36 minutos.<\/p>\n<p>Quanto tempo demoraria a fazer o mesmo percurso se andasse a uma velocidade m\u00e9dia de 45 km\/h?<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Come\u00e7ando por tabelar os dados, temos:<\/p>\n<table style=\"width: 60%;\">\n<tfoot>\n<tr>\n<td style=\"text-align: right;\">Comprimento do percurso (em km)<\/td>\n<td>45<\/td>\n<td>45<\/td>\n<\/tr>\n<\/tfoot>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">Velocidade m\u00e9dia (em km\/h) &#8211; <strong>\\(v\\)<\/strong><\/td>\n<td>75<\/td>\n<td>45<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">Tempo gasto no percurso (em horas) &#8211;<strong>\u00a0\\(t\\)<\/strong><\/td>\n<td>0,6<\/td>\n<td>?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Ora, as grandezas\u00a0\\(v\\) e\u00a0\\(t\\) s\u00e3o inversamente proporcionais, pois o produto das correspondentes medidas \u00e9 constante:\u00a0\\(v \\times t = 45\\).<\/p>\n<p>Assim, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{45 \\times t = 45}&amp; \\Leftrightarrow &amp;{t = \\frac{{45}}{{45}}}\\\\{}&amp; \\Leftrightarrow &amp;{t = 1}\\end{array}\\]<\/p>\n<p>Portanto, se o comboio andasse a uma velocidade m\u00e9dia de 45 km\/h, demoraria 1 hora a fazer o mesmo percurso.<\/p>\n<p><strong>Nota<\/strong>:\u00a0\\(36\\;min = 36 \\times \\frac{1}{{60}}\\;h = \\frac{{6 \\times 6}}{{6 \\times 10}}\\;h = 0,6\\;h\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14604' onClick='GTTabs_show(0,14604)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um comboio que anda \u00e0 velocidade m\u00e9dia de 75 km\/h faz um certo percurso em 36 minutos. Quanto tempo demoraria a fazer o mesmo percurso se andasse a uma velocidade m\u00e9dia&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14606,"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-14604","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":1701,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag102-6a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14604","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=14604"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14604\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14606"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14604"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14604"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14604"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}