{"id":3508,"date":"2022-12-23T18:45:00","date_gmt":"2022-12-23T22:45:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=3508"},"modified":"2024-10-25T09:55:27","modified_gmt":"2024-10-25T13:55:27","slug":"when-did-the-snow-start-to-fall","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=3508","title":{"rendered":"When did the snow start to fall?"},"content":{"rendered":"\n<p>One day sometime before 12 noon, the snow started to fall. A snow plower started to remove snow from the streets at 12 o&#8217;clock. In the first hour, it advanced 6 miles; in the second hour, it advanced 3 miles. When did the snow start to fall? Click <a href=\"javascript:toggle_visibility('sol-snow');\">here<\/a> for the solution.<\/p>\n\n\n\n<div id=\"sol-snow\" name=\"sol-snow\" style=\"display:none\">\n\n\n\n<p><strong>Solution<\/strong>: Assume that the snow was falling at a constant rate of $r$ inches per hour, and the snow plower can remove snow from the streets at a constant rate. The width of the snow plower is $w$ inches. Assume the snow starts to fall $x$ hours before 12 noon. Therefore, we have the following observations:<\/p>\n\n\n\n<p>At 12 o&#8217;clock, $x\\times r$ inches of snow on the unplowed streets<\/p>\n\n\n\n<p>At 13 o&#8217;clock, $(x+1)\\times r$ inches of snow on the unplowed streets<\/p>\n\n\n\n<p>At 14 o&#8217;clock, $(x+2)\\times r$ inches of snow on the unplowed streets<\/p>\n\n\n\n<p>The total volume of snow removed in the first hour would be:<\/p>\n\n\n\n<p>$$6\\times w\\times\\dfrac{x\\times r + (x+1)\\times r}{2}\\ \\ \\ \\ \\ {miles\\times inch^2}$$<\/p>\n\n\n\n<p>The total volume of snow removed in the second hour would be:<\/p>\n\n\n\n<p>$$3\\times w\\times\\dfrac{(x+1)\\times r + (x+2)\\times r}{2}\\ \\ \\ \\ \\ {miles\\times inch^2}$$<\/p>\n\n\n\n<p>Because the snow plower removes snow at a constant rate, we have: <\/p>\n\n\n\n<p>$$6\\times w\\times\\dfrac{x\\times r + (x+1)\\times r}{2}=3\\times w\\times\\dfrac{(x+1)\\times r + (x+2)\\times r}{2}$$<\/p>\n\n\n\n<p>Solving the above equation, we have $x=\\dfrac{1}{2}$. Therefore the snow started to fall at $\\boxed{11:30 AM}$.<\/p>\n\n\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>One day sometime before 12 noon, the snow started to fall. A snow plower started to remove snow from the streets at 12 o&#8217;clock. In the first hour, it advanced 6 miles; in the second hour, it advanced 3 miles. &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=3508\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[13],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3508"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3508"}],"version-history":[{"count":16,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3508\/revisions"}],"predecessor-version":[{"id":3524,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3508\/revisions\/3524"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}