Two butterflies simultaneously leave an aster flowerbed and fly to a rose flowerbed. One butterfly flies 10 m\/min faster than the other, and so lands on a rose 1 minute earlier. Find the speed of each butterfly if the flowerbeds are 560m apart<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The Correct Answer is :Slower butterfly: 70 m\/min<\/strong><\/p>\n\n\n\n faster butterflies:80m\/min<\/strong><\/mark><\/p>\n\n\n\n To solve the problem, we can define the speeds of the two butterflies and use the information provided to set up equations.<\/p>\n\n\n\n Let:<\/p>\n\n\n\n The distance between the flowerbeds is 560 meters. We can express the time taken by each butterfly to reach the rose flowerbed as follows:<\/p>\n\n\n\n According to the problem, the faster butterfly arrives 1 minute earlier than the slower butterfly: Substituting the expressions for ( t_1 ) and ( t_2 ) into the equation: To eliminate the fractions, multiply through by ( v(v + 10) ): Rearranging the equation gives: We can use the quadratic formula: Calculating the positive root: Thus, the speeds of the butterflies are:<\/p>\n\n\n\n In conclusion, using algebraic methods and the relationship between distance, speed, and time, we can determine the speeds of the two butterflies based on the conditions given in the problem.<\/p>\n","protected":false},"excerpt":{"rendered":" Two butterflies simultaneously leave an aster flowerbed and fly to a rose flowerbed. One butterfly flies 10 m\/min faster than the other, and so lands on a rose 1 minute earlier. Find the speed of each butterfly if the flowerbeds are 560m apart The Correct Answer and Explanation is : The Correct Answer is :Slower […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-148557","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148557","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=148557"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148557\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=148557"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=148557"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=148557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Define Variables<\/h3>\n\n\n\n
\n
Step 2: Set Up the Equations<\/h3>\n\n\n\n
\n
[
t_1 = \\frac{560}{v}
]<\/li>\n\n\n\n
[
t_2 = \\frac{560}{v + 10}
]<\/li>\n<\/ul>\n\n\n\n
[
t_1 – t_2 = 1
]<\/p>\n\n\n\nStep 3: Substitute and Simplify<\/h3>\n\n\n\n
[
\\frac{560}{v} – \\frac{560}{v + 10} = 1
]<\/p>\n\n\n\n
[
560(v + 10) – 560v = v(v + 10)
]
[
5600 = v^2 + 10v
]<\/p>\n\n\n\nStep 4: Rearrange into a Quadratic Equation<\/h3>\n\n\n\n
[
v^2 + 10v – 5600 = 0
]<\/p>\n\n\n\nStep 5: Solve the Quadratic Equation<\/h3>\n\n\n\n
[
v = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
]
where ( a = 1 ), ( b = 10 ), and ( c = -5600 ):
[
v = \\frac{-10 \\pm \\sqrt{10^2 – 4 \\cdot 1 \\cdot (-5600)}}{2 \\cdot 1}
]
[
v = \\frac{-10 \\pm \\sqrt{100 + 22400}}{2}
]
[
v = \\frac{-10 \\pm \\sqrt{22500}}{2}
]
[
v = \\frac{-10 \\pm 150}{2}
]<\/p>\n\n\n\n
[
v = \\frac{140}{2} = 70 \\, \\text{m\/min}
]<\/p>\n\n\n\nStep 6: Calculate Speeds<\/h3>\n\n\n\n
\n
Conclusion<\/h3>\n\n\n\n
\n