{"id":"cb_question_bank:4c8bea11-e38b-4d52-a733-4fe399e198fc","source_id":"cb_question_bank","source_item_id":"4c8bea11-e38b-4d52-a733-4fe399e198fc","external_id":"20220edf-4df0-47cb-bce6-798d01c48907","ibn":null,"question_id":"74c03c21","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A bus traveled on the highway and on local roads to complete a trip of 160 miles . The trip took 4 hours . The bus traveled at an average speed of 55 miles per hour left parenthesis mph right parenthesis on the highway and an average speed of 25 mph on local roads. If x is the time, in hours, the bus traveled on the highway and y is the time, in hours, it traveled on local roads, which system of equations represents this situation?","stimulus":"","stimulus_html":null,"stem_html":"

A bus traveled on the highway and on local roads to complete a trip of 160 miles. The trip took 4 hours. The bus traveled at an average speed of 55 miles per hour mph on the highway and an average speed of 25 mph on local roads. If x\n is the time, in hours, the bus traveled on the highway and y\n is the time, in hours, it traveled on local roads, which system of equations represents this situation?

","rationale_html":"

Choice B is correct. If the bus traveled at an average speed of 55 miles per hour mph on the highway for x\n hours, then the bus traveled \n\t55\n\tx\n\n miles on the highway. If the bus traveled at an average speed of 25 mph on local roads for y\n hours, then the bus traveled \n\t25\n\ty\n\n miles on local roads. It's given that the trip was 160\n miles. This can be represented by the equation 55x+25y=160. It's also given that the trip took 4\n hours. This can be represented by the equation \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\n\t=\n\t4\n\n. Therefore, the system consisting of the equations 55x+25y=160 and \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\n\t=\n\t4\n\n represents this situation.

\n

Choice A is incorrect. This system of equations represents a situation where the trip was 4\n miles and took 160\n hours.

\n

Choice C is incorrect. This system of equations represents a situation where the trip was 4\n miles and took 160\n hours, and the bus traveled at an average speed of 25 mph on the highway and 55 mph on local roads.

\n

Choice D is incorrect. This system of equations represents a situation where the bus traveled at an average speed of 25 mph on the highway and 55 mph on local roads.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"

55x+25y=4
x+y=160

","ord":0},{"label":"B","content_html":"

55x+25y=160
x+y=4

","ord":1},{"label":"C","content_html":"

25x+55y=4
x+y=160

","ord":2},{"label":"D","content_html":"

25x+55y=160
x+y=4

","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}}