{"id":"aqua_rat:b9f85954b8ac4b8795b779a477b5d62d","source_id":"aqua_rat","source_item_id":"b9f85954b8ac4b8795b779a477b5d62d","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"A cycled from P to Q at 10 kmph and returned at the rate of 9 kmph. B cycled both ways at 12 kmph. In the whole journey B took 10 minutes less than A. Find the distance between P and Q.","stimulus":"","stimulus_html":null,"stem_html":"<p>A cycled from P to Q at 10 kmph and returned at the rate of 9 kmph. B cycled both ways at 12 kmph. In the whole journey B took 10 minutes less than A. Find the distance between P and Q.</p>","rationale_html":"<p>A -time = d/10 + d/9 = 19d/90 hours</p><p>B -time = 2d/12 = d/6 hours</p><p>10 min = 1/6 hours</p><p>Thus 19d/90 - d/6 = 1/6</p><p>(19d-15d)/90 = 1/6</p><p>4d/90 = 1/6</p><p>thus d= 15/4 km = 3.75km</p><p>C</p>","correct_answer":["C"],"equiv_key":"e0e7098cb4d5195a175252ae","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>1.75km</p>","ord":0},{"label":"B","content_html":"<p>2.75km</p>","ord":1},{"label":"C","content_html":"<p>3.75km</p>","ord":2},{"label":"D","content_html":"<p>4.75km</p>","ord":3},{"label":"E","content_html":"<p>5.75km</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}