{"id":"cb_question_bank:3a28cf2a-ba3c-4764-b859-21d5d0fe8198","source_id":"cb_question_bank","source_item_id":"3a28cf2a-ba3c-4764-b859-21d5d0fe8198","external_id":"816cb6b4-6796-4c47-ae29-2ccb52e5c8ab","ibn":null,"question_id":"ee439cff","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under 220 miles. Rhett drove at an average speed of 35 miles per hour left parenthesis mph right parenthesis , and Jessica drove at an average speed of 40 mph . Which of the following inequalities represents this situation, where r is the number of hours Rhett drove and j is the number of hours Jessica drove?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under <math alttext=\"220\"><mn>220</mn>\n</math> miles. Rhett drove at an average speed of <math alttext=\"35 miles per hour left parenthesis mph right parenthesis\"><mrow><mn>35</mn></mrow><mo>&nbsp;</mo><mtext>miles</mtext><mo>&nbsp;</mo><mtext>per</mtext><mo>&nbsp;</mo><mtext>hour</mtext><mo>&nbsp;</mo><mfenced><mtext>mph</mtext></mfenced></math>, and Jessica drove at an average speed of <math alttext=\"40 mph\"><mrow><mn>40</mn></mrow><mo>&nbsp;</mo><mtext>mph</mtext></math>. Which of the following inequalities represents this situation, where <math alttext=\"r\"><mi>r</mi>\n</math> is the number of hours Rhett drove and <math alttext=\"j\"><mi>j</mi>\n</math> is the number of hours Jessica drove?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It’s given that Rhett drove at an average speed of <math alttext=\"35\"><mn>35</mn>\n</math> miles per hour and that he drove for <math alttext=\"r\"><mi>r</mi>\n</math> hours. Multiplying <math alttext=\"35\"><mn>35</mn>\n</math> miles per hour by <math alttext=\"r\"><mi>r</mi>\n</math> hours yields <math alttext=\"35 r\"><mrow>\n\t<mn>35</mn>\n\t<mi>r</mi>\n</mrow>\n</math> miles, or the distance that Rhett drove. It’s also given that Jessica drove at an average speed of <math alttext=\"40\"><mn>40</mn>\n</math> miles per hour and that she drove for <math alttext=\"j\"><mi>j</mi>\n</math> hours. Multiplying <math alttext=\"40\"><mn>40</mn>\n</math> miles per hour by <math alttext=\"j\"><mi>j</mi>\n</math> hours yields <math alttext=\"40 j\"><mn>40</mn><mi>j</mi></math> miles, or the distance that Jessica drove. The total distance, in miles, that Rhett and Jessica drove can be represented by the expression <math alttext=\"35 r plus 40 j\"><mn>35</mn><mi>r</mi><mo>+</mo><mn>40</mn><mi>j</mi></math>. It’s given that the total distance they drove was under <math alttext=\"220\"><mn>220</mn>\n</math> miles. Therefore, the inequality <math alttext=\"35 r plus 40 j less than 220\"><mn>35</mn><mi>r</mi><mo>+</mo><mn>40</mn><mi>j</mi><mo>&lt;</mo><mn>220</mn></math> represents this situation.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This inequality represents a situation in which the total distance Rhett and Jessica drove was over, rather than under, <math alttext=\"220\"><mn>220</mn>\n</math> miles.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This inequality represents a situation in which Rhett drove at an average speed of <math alttext=\"40\"><mn>40</mn>\n</math>, rather than <math alttext=\"35\"><mn>35</mn>\n</math>, miles per hour, Jessica drove at an average speed of <math alttext=\"35\"><mn>35</mn>\n</math>, rather than <math alttext=\"40\"><mn>40</mn>\n</math>, miles per hour, and the total distance they drove was over, rather than under, <math alttext=\"220\"><mn>220</mn>\n</math> miles.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This inequality represents a situation in which Rhett drove at an average speed of <math alttext=\"40\"><mn>40</mn>\n</math>, rather than <math alttext=\"35\"><mn>35</mn>\n</math>, miles per hour, and Jessica drove at an average speed of <math alttext=\"35\"><mn>35</mn>\n</math>, rather than <math alttext=\"40\"><mn>40</mn>\n</math>, miles per hour.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.820000+00:00","source_updated_at":"2023-08-02T20:25:59.820000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"35 r plus 40 j greater than 220\"><mrow><mn>35</mn></mrow><mi>r</mi><mo>+</mo><mrow><mn>40</mn></mrow><mi>j</mi><mo>&gt;</mo><mrow><mn>220</mn></mrow></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"35 r plus 40 j less than 220\"><mrow><mn>35</mn></mrow><mi>r</mi><mo>+</mo><mrow><mn>40</mn></mrow><mi>j</mi><mo>&lt;</mo><mrow><mn>220</mn></mrow></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"40 r plus 35 j greater than 220\"><mrow><mn>40</mn></mrow><mi>r</mi><mo>+</mo><mrow><mn>35</mn></mrow><mi>j</mi><mo>&gt;</mo><mrow><mn>220</mn></mrow></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"40 r plus 35 j less than 220\"><mrow><mn>40</mn></mrow><mi>r</mi><mo>+</mo><mrow><mn>35</mn></mrow><mi>j</mi><mo>&lt;</mo><mrow><mn>220</mn></mrow></math></p>","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}}