{"id":6772,"date":"2011-04-13T23:43:20","date_gmt":"2011-04-13T22:43:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6772"},"modified":"2022-01-18T02:14:22","modified_gmt":"2022-01-18T02:14:22","slug":"quatro-amigos-fizeram-uma-viagem-de-automovel","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6772","title":{"rendered":"Quatro amigos fizeram uma viagem de autom\u00f3vel"},"content":{"rendered":"<p><ul id='GTTabs_ul_6772' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6772' class='GTTabs_curr'><a  id=\"6772_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6772' ><a  id=\"6772_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_6772'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/Road-Trip-.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12281\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12281\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/Road-Trip-.png\" data-orig-size=\"600,366\" 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=\"Viagem\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/Road-Trip-.png\" class=\"alignright size-medium wp-image-12281\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/Road-Trip--300x183.png\" alt=\"Viagem\" width=\"300\" height=\"183\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/Road-Trip--300x183.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/Road-Trip-.png 600w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Quatro amigos fizeram uma viagem de autom\u00f3vel.<\/p>\n<p>Como o percurso era longo, cada um conduziu uma parte.<\/p>\n<p>A Marta conduziu $\\frac{1}{3}$ do percurso, o Francisco durante $\\frac{1}{5}$ do percurso, a Cl\u00e1udia durante $\\frac{3}{10}$ do percurso e o Lu\u00eds conduziu os restantes 500 km.<\/p>\n<p>De quantos quil\u00f3metros foi a viagem?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6772' onClick='GTTabs_show(1,6772)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6772'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A Marta conduziu $\\frac{1}{3}$ do percurso, o Francisco durante $\\frac{1}{5}$ do percurso, a Cl\u00e1udia durante $\\frac{3}{10}$ do percurso e o Lu\u00eds conduziu os restantes 500 km.<\/p>\n<\/blockquote>\n<p>Seja x o n\u00famero de quil\u00f3metros da viagem.<\/p>\n<p>O n\u00famero de quil\u00f3metros que cada um um dos amigos conduziu foi:<\/p>\n<ul>\n<li>Marta: $\\frac{x}{3}$<\/li>\n<li>Francisco: $\\frac{x}{5}$<\/li>\n<li>Cl\u00e1udia: $\\frac{3x}{10}$<\/li>\n<li>Lu\u00eds: $500$<\/li>\n<\/ul>\n<p>Assim, temos:<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n\\frac{x}{\\underset{(10)}{\\mathop{3}}\\,}+\\frac{x}{\\underset{(6)}{\\mathop{5}}\\,}+\\frac{3x}{\\underset{(3)}{\\mathop{10}}\\,}+\\underset{(30)}{\\mathop{500}}\\,=\\underset{(30)}{\\mathop{x}}\\, &amp; \\Leftrightarrow\u00a0 &amp; 10x+6x+9x+15000=30x\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -5x=-15000\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=3000\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Portanto, a viagem foi de 3000 km.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6772' onClick='GTTabs_show(0,6772)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Quatro amigos fizeram uma viagem de autom\u00f3vel. Como o percurso era longo, cada um conduziu uma parte. A Marta conduziu $\\frac{1}{3}$ do percurso, o Francisco durante $\\frac{1}{5}$ do percurso, a Cl\u00e1udia&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20583,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,159],"tags":[425],"series":[],"class_list":["post-6772","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-do-1--grau","tag-equacoes"],"views":2886,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8V2Pag056-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6772","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=6772"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6772\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20583"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6772"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}