{"id":"cb_question_bank:b6b09f80-8ea4-4fe0-b37b-11fd5e278bf5","source_id":"cb_question_bank","source_item_id":"b6b09f80-8ea4-4fe0-b37b-11fd5e278bf5","external_id":null,"ibn":"028911-DC","question_id":"f6cbb04a","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.A.","skill":"Ratios, rates, proportional relationships, and units","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The equation above can be used to calculate the distance d , in miles, traveled by a car moving at a speed of 55 miles per hour over a period of t hours. For any positive constant k , the distance the car would have traveled after 9 k hours is how many times the distance the car would have traveled after 3 k hours?","stimulus":"d equals, 55 t","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/79f6a78dabebf465d79b92e8ddc82513fd6948542173488df717e5ccd81356dc\" alt=\"d equals, 55 t\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The equation above can be used to calculate the distance <span class=\"italic\">d</span>, in miles, traveled by a car moving at a speed of 55&nbsp;miles per hour over a period of <span class=\"italic\">t</span> hours. For any positive constant <span class=\"italic\">k</span>, the distance the car would have traveled after <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fc4a4acd928137fb39f5d79eb686fd6f00365f0a5a0308eb3eaee76dffc48587\" alt=\"9 k\"></span> hours is how many times the distance the car would have traveled after <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94e5f999a1c5fb935c7653bc848c08325dc7c96d0f7d111e89eb510d02dd91a8\" alt=\"3 k\"></span>&nbsp;hours?</p>\n","rationale_html":"<p>Choice A is correct. Since the distance is equal to the amount of time multiplied by a constant, the given equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/79f6a78dabebf465d79b92e8ddc82513fd6948542173488df717e5ccd81356dc\" alt=\"d equals 55 t \"></span> represents a proportional relationship between distance and time in this situation. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ea736d3db16aa718582b581ca5cef5aad52c4f7dfed43cb52dffc1e972ccb0a\" alt=\"9 k equals, 3 times 3 k\"></span>, the time when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/50afca2e159f2c3b3957478d9012b4ce733d61828213d145e4d3766c09404cf8\" alt=\"t equals 9 k \"></span> hours is 3 times the time when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a0564ff07149e63d1303977399cf7add44f912f2038a2badd5d02bec3cefcea9\" alt=\"t equals 3 k \"></span> hours. Therefore, the distance traveled after <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fc4a4acd928137fb39f5d79eb686fd6f00365f0a5a0308eb3eaee76dffc48587\" alt=\"9 k\"></span> hours is 3 times the distance after <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94e5f999a1c5fb935c7653bc848c08325dc7c96d0f7d111e89eb510d02dd91a8\" alt=\"3 k\"></span> hours.</p><p>Choices B and D are incorrect and may result from interpreting the proportional relationship between time and distance as additive rather than multiplicative. Choice C is incorrect and may result from an arithmetic error.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.623000+00:00","source_updated_at":"2023-08-02T20:25:59.623000+00:00","options":[{"label":"A","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b35ae18904fb781bd47e663cf02b992965491e4f50b31194e7d69870143879cd\" alt=\"3\"></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3ba1d0c351ba804f1e264fab3db5d1fb3d2696b974be16e1a3b091433eb096d6\" alt=\"6\"></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94e5f999a1c5fb935c7653bc848c08325dc7c96d0f7d111e89eb510d02dd91a8\" alt=\"3k\"></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/410f7eb30c5d74ca608aaf3e364e0d02b8f2023131b29324ac29a32d285db3b4\" alt=\"6 k\"></span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}