{"id":413,"date":"2022-04-13T10:55:35","date_gmt":"2022-04-13T10:55:35","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=413"},"modified":"2025-03-20T06:36:41","modified_gmt":"2025-03-20T06:36:41","slug":"v-2-rate-of-travel-word-problems","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/v-2-rate-of-travel-word-problems\/","title":{"rendered":"V.2 Rate of travel: word problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Rate of travel: word problems<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-203290aba75681a4fb07a0852f132b50\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-09b90ecb46c16810b14a18d2b092598d\" style=\"color:#000060\">\ud83d\udd0d<strong>Understanding Rate of Travel<\/strong><\/h3>\n\n\n\n<p class=\"has-large-font-size\"><strong>Rate<\/strong> refers to how fast something moves, typically measured as <strong>distance per unit of time<\/strong> (e.g., km\/h, m\/s).<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>The basic formula is: <\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Distance = Rate \u00d7 Time<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Rate<\/strong> = Distance \u00f7 Time<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Time<\/strong> = Distance \u00f7 Rate<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-0a1784372aee989241914acb89d87818\" style=\"color:#000060\">\ud83d\udd0d<strong>Types of Word Problems<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Direct travel:<\/strong> One vehicle travels a certain distance at a constant speed.<\/li>\n\n\n\n<li><strong>Round trips:<\/strong> Going to a place and returning (different speeds possible).<\/li>\n\n\n\n<li><strong>Two objects moving toward\/away from each other:<\/strong> Boats in a river, cars on a road, etc.<\/li>\n\n\n\n<li><strong>Catch-up problems:<\/strong> One object starts later and tries to catch up to the first.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-91abfd2643a7491d6db80ef34059d4d0\" style=\"color:#000060\">\ud83d\udee0\ufe0f<strong>Solving Word Problems Step-by-Step<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Read the problem carefully<\/strong> \u2014 Identify what\u2019s given (distance, rate, time) and what you need to find.<\/li>\n\n\n\n<li><strong>Define variables<\/strong> \u2014 Let r, t, or d represent unknowns.<\/li>\n\n\n\n<li><strong>Set up an equation<\/strong> \u2014 Use d=rtd and plug in the known values.<\/li>\n\n\n\n<li><strong>Solve the equation<\/strong> \u2014 Apply algebraic methods.<\/li>\n\n\n\n<li><strong>Check your answer<\/strong> \u2014 Make sure it makes sense in context (e.g., a negative speed doesn\u2019t work).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-a1789ccf362518705b0c93268c258964\" style=\"color:#000060\">\ud83e\udde0<strong>Common Example Problems<\/strong><\/h3>\n\n\n\n<p class=\"has-large-font-size\"><strong>Single journey:<\/strong> A car travels 180 km at 60 km\/h. How long does it take?<\/p>\n\n\n\n<p class=\"has-large-font-size\">t = 180\/60 = 3hours<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Round trip:<\/strong> A boat travels 30 km downstream (with the current) at 10 km\/h and returns against the current at 6 km\/h. How long is the total trip?<\/p>\n\n\n\n<p class=\"has-large-font-size\">Downstream: t<sub>1<\/sub> = 30\/10 = 3 hours<\/p>\n\n\n\n<p class=\"has-large-font-size\">Upstream: t<sub>2<\/sub> = 30\/6 = 5 hours<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Total time<\/strong> = 3 + 5 = <strong>8 hours<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Catch-up problem:<\/strong> A cyclist leaves a town at 20 km\/h. Two hours later, a car leaves the same place at 50 km\/h. How long until the car catches up?<\/p>\n\n\n\n<p class=\"has-large-font-size\">Distance covered by the cyclist: 20t<\/p>\n\n\n\n<p class=\"has-large-font-size\">Distance covered by the car: 50 (t\u22122)<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Set up equation: <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">20t = 50 (t\u22122)<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Solve: <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">20t = 50t \u2212 100\u2005\u200a\u27f9\u2005\u200a30t = 100\u2005\u200a\u27f9\u2005\u200at =100\/30 \u2248 3.33\u2009hours<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dac9fb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-2abc87771bac351af73f6bf28c824914\" style=\"color:#b00012\"><strong> \ud83c\udfaf After spending the winter in Clay County, two flocks of birds are now migrating home. The first flock flies due east at 45 kilometres per hour, and the second flies west at 65 kilometres per hour. In how much time will they be 750 kilometres apart?<\/strong><\/p>\n\n\n\n<p>\ud83c\udfaf <em>If necessary, round your answer to the nearest minute.<\/em><\/p>\n\n\n\n<p>______&nbsp;hours and__________&nbsp;&nbsp;minutes<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The distance to be covered is 750 kilometres.<\/li>\n\n\n\n<li>The first flock&#8217;s rate is 45 kilometres per hour. The second flock&#8217;s rate is 65 kilometres per hour. Together, they are increasing the gap between them at a rate of 45 + 65 = 110 kilometres per hour.<\/li>\n\n\n\n<li>Now write an equation and solve for t.<\/li>\n\n\n\n<li>d = rt<\/li>\n\n\n\n<li>750 = 110t Plug in d = 750 and r = 110<\/li>\n\n\n\n<li>6.818181\u2026 = t Divide both sides by 110<\/li>\n\n\n\n<li>The units for t are hours. Convert the units to be in hours and minutes, rounded to the nearest minute.<\/li>\n\n\n\n<li>The whole-number portion is 6. That is 6 full hours.<\/li>\n\n\n\n<li>Convert the decimal portion.<\/li>\n\n\n\n<li>0.818181\u2026 <s>hours<\/s> \u00d7 60 minutes\/1 hour \u2248 49 minutes<\/li>\n\n\n\n<li>So, t is approximately 6 hours and 49 minutes.<\/li>\n\n\n\n<li>The flocks of birds will be 750 kilometres apart in about 6 hours and 49 minutes.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b8fdaf\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-58fdc01f45cec9566460a7b0207679a6\" style=\"color:#b00012\"><strong> \ud83c\udfaf A Coast Guard rescue craft just picked up the captain of a disabled sailboat. The rescue craft is now heading back to shore at a rate of 57 kilometres per hour. Meanwhile, the sailboat is drifting in the other direction at 6 kilometres per hour. How long will it be before the rescue craft is 29 kilometres from the sailboat?<\/strong><\/p>\n\n\n\n<p>\ud83c\udfaf <em>If necessary, round your answer to the nearest minute.<\/em><\/p>\n\n\n\n<p>&nbsp;___hours and&nbsp;____&nbsp;minutes<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The distance to be covered is 29 kilometres.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The sailboat&#8217;s rate is 6 kilometres per hour. The rescue craft&#8217;s rate is 57 kilometres per hour. Together, they are increasing the gap between them at a rate of&nbsp;6 + 57 = 63&nbsp;kilometres per hour.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Now write an equation and solve for&nbsp;<em>t<\/em>.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>d<\/em>&nbsp;=&nbsp;<em>rt<\/em><\/li>\n\n\n\n<li>29&nbsp;=&nbsp;63<em>tPlug in&nbsp;d&nbsp;= 29 and&nbsp;r&nbsp;= 63<\/em><\/li>\n\n\n\n<li>0.460317&#8230;&nbsp;=&nbsp;<em>tDivide both sides by 63<\/em><\/li>\n\n\n\n<li>The units for&nbsp;<em>t<\/em>&nbsp;are hours. Convert the units to be in hours and minutes, rounded to the nearest minute.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>0.460317&#8230;&nbsp;<s>hours<\/s>&nbsp;\u00d7&nbsp;60 minutes\/ 1&nbsp;<s>hour<\/s><\/td><td>&nbsp;\u2248&nbsp;<\/td><td>28 minutes<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>So,&nbsp;<em>t<\/em>&nbsp;is approximately 28 minutes.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The rescue craft will be 29 kilometres from the sailboat in about 28 minutes.<img decoding=\"async\" src=\"\" alt=\"\"><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#fdd3b5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-653ba0f613b09ed1259ef63c04d1c264\" style=\"color:#b00012\"><strong>\ud83c\udfaf A ranch hand herded his cattle to some grazing land. Then he began riding back to the ranch, which is due west, at 5 kilometres per hour. Simultaneously, the cows began moving away from him, too, headed due east at 3 kilometres per hour. How long did it take for the herd and the ranch hand to be 2 kilometres apart?<\/strong><\/p>\n\n\n\n<p>\ud83c\udfaf <em>If necessary, round your answer to the nearest minute.<\/em><\/p>\n\n\n\n<p>&nbsp;_____hours and&nbsp;_____ &nbsp;minutes<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The distance to be covered is 2 kilometres.<\/li>\n\n\n\n<li>The herd&#8217;s rate is 3 kilometres per hour. The ranch hand&#8217;s rate is 5 kilometres per hour. Together, they are increasing the gap between them at a rate of&nbsp;3 + 5 = 8&nbsp;kilometres per hour.<\/li>\n\n\n\n<li>Now write an equation and solve for&nbsp;<em>t<\/em>.<\/li>\n\n\n\n<li><em>d<\/em>&nbsp;=&nbsp;<em>rt<\/em><br>2&nbsp;=&nbsp;8<em>tPlug in&nbsp;d&nbsp;= 2 and&nbsp;r&nbsp;= 8<\/em><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><\/td><td>28<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&nbsp;=&nbsp;<em>tDivide both sides by 8<\/em><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><\/td><td>14<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&nbsp;=&nbsp;<em>tSimplify<\/em><\/li>\n\n\n\n<li>The units for&nbsp;<em>t<\/em>&nbsp;are hours. Convert the units to be in hours and minutes.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>14<s>of an hour<\/s>&nbsp;\u00d7&nbsp;60 minutes\/ 1&nbsp;<s>hour<\/s><\/td><td>&nbsp;=&nbsp;<\/td><td>15 minutes<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>So,&nbsp;<em>t<\/em>&nbsp;is 15 minutes.<\/li>\n\n\n\n<li>The herd and the ranch hand were 2 kilometres apart in 15 minutes.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/88914\/134\/889\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-148.png\" alt=\"\" class=\"wp-image-7443\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-148.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-148-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-148-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/38355\/614\/901\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-167.png\" alt=\"\" class=\"wp-image-7444\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-167.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-167-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-167-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Rate of travel: word problems key notes : \ud83d\udd0dUnderstanding Rate of Travel Rate refers to how fast something moves, typically measured as distance per unit of time (e.g., km\/h, m\/s). The basic formula is: Distance = Rate \u00d7 Time Rate = Distance \u00f7 Time Time = Distance \u00f7 Rate \ud83d\udd0dTypes of Word Problems \ud83d\udee0\ufe0fSolving Word<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/v-2-rate-of-travel-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;V.2 Rate of travel: word problems&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-413","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=413"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/413\/revisions"}],"predecessor-version":[{"id":17650,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/413\/revisions\/17650"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}