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miles per hour. \nAt what time does Dani arrive at work?","markscheme":"- $\\text{time} = \\frac{63}{27} = 2.33...$ hours M1\n- $2.33...$ hours = 2 hours 20 minutes M1\n- $08:00 + 2:20 = 10:20$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates travel time as 2.33... hours or 2 hours 20 minutes.","code":"M"},{"id":"p2","marks":1,"description":"Correct arrival time of 10:20.","code":"A"}],"finalAnswers":["10:20"],"generatedAt":"2026-05-07T01:54:16.909Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":74},"walkthroughVideo":null},{"id":"f1e4cd96-ef4b-4d2e-ae14-9141db088e33","revisionId":"db0ea6dd-aa26-4802-85b2-ee9c195be518","questionNumber":"9","questionType":"LA","specification":"Anthony travels from Newcastle to Manchester at an average speed of 65 miles per hour. \nThe journey takes him 2 hours and 15 minutes.\n\nDeclan makes the same journey in 2 hours and 35 minutes.","difficulty":3,"difficultyBand":"medium","totalMarks":5,"sourceTitle":"Speed and Density","calculatorUse":null,"isCalculation":true,"parts":[{"id":"c7b6cba7-e2de-4210-a4fd-cd2b6c8490aa","label":"a","content":"Work out Declan's average speed for the journey.","markscheme":"- Distance = $65 \\times 2.25 = 146.25$ miles M1\n- Declan's time = $2 + \\frac{35}{60} = 2.583...$ hours M1\n- Speed = $\\frac{146.25}{2.583...}$ M1\n- $56.6$ mph A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Calculates the distance of the journey (146.25 miles).","code":"M"},{"id":"p2","marks":1,"description":"Converts Declan's time to decimal hours (approx 2.583).","code":"M"},{"id":"p3","marks":1,"description":"Applies speed = distance / time for Declan.","code":"M"},{"id":"p4","marks":1,"description":"Final answer of 56.6 mph (or equivalent accuracy).","code":"A"}],"finalAnswers":["56.6"],"generatedAt":"2026-05-07T01:54:16.909Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"distance_then_speed","label":"Find distance, then speed","steps":[{"type":"text","order":0,"title":"Convert Anthony's time","content":"Convert Anthony's journey time into hours:\n\n$$2+\\frac{15}{60}=2.25\\text{ hours}$$\n\nAnthony travels the same Newcastle-to-Manchester distance as Declan, so this distance will also be Declan's distance.","highlights":[{"text":"The journey takes him 2 hours and 15 minutes.","location":"specification"},{"text":"Declan makes the same journey","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$d=\\htmlData{anchor=distance_sub}{65\\times 2.25}$"},{"latex":"$$\\htmlData{anchor=distance_result}{d=146.25\\text{ miles}}$"}],"highlights":[{"color":"amber","style":"text-color","anchor":"distance_sub"},{"color":"green","style":"text-color-with-background","anchor":"distance_result"}],"connections":[{"to":"distance_result","from":"distance_sub","color":"sky","label":"calculate"}]},"order":1,"title":"Calculate the distance","description":"Use distance = speed × time. This substitution and calculation earns the distance method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=time_expression}{t=\\left(2+\\frac{35}{60}\\right)\\text{ hours}}$"},{"latex":"$$\\htmlData{anchor=time_result}{t=2.5833\\ldots\\text{ hours}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"time_expression"},{"color":"green","style":"text-color-with-background","anchor":"time_result"}],"connections":[{"to":"time_result","from":"time_expression","color":"sky","label":"calculate"}]},"order":3,"title":"Find the journey time","description":"Convert the 35 minutes to hours by dividing by 60, then add it to the 2 hours. This complete time calculation earns the second method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=speed_formula}{v=\\frac{d}{t}}$"},{"latex":"$$\\htmlData{anchor=speed_substitution}{v=\\frac{146.25}{2.5833\\ldots}}$"},{"latex":"$$\\htmlData{anchor=speed_result}{v=56.6129\\ldots\\text{ mph}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"speed_formula"},{"color":"amber","style":"text-color-with-background","anchor":"speed_substitution"},{"color":"green","style":"text-color","anchor":"speed_result"}],"connections":[{"to":"speed_substitution","from":"speed_formula","color":"sky","label":"substitute"},{"to":"speed_result","from":"speed_substitution","color":"green","label":"calculate"}]},"order":5,"title":"Calculate the speed","description":"Use average speed = distance divided by time, then substitute the distance and Declan's time. This substitution earns the third method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=round_start}{v=56.6129\\ldots\\text{ mph}}$"},{"latex":"$$\\htmlData{anchor=round_answer}{\\boxed{v=56.6\\text{ mph}}}$"}],"highlights":[{"color":"amber","style":"text-color","anchor":"round_start"},{"color":"green","style":"text-color-with-background","anchor":"round_answer"}],"connections":[{"to":"round_answer","from":"round_start","color":"green","label":"round"}]},"order":6,"title":"Round the answer","description":"Round the unrounded speed to one decimal place. This earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-21T04:11:47.332Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"25b9ce7c-172d-41ce-866e-6a2a15898655","label":"b","content":"If Declan took different roads than Anthony, how could this affect your answer to part (a)?","markscheme":"- If the distance was increased the speed would be higher (or vice versa) C1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"States that a change in distance would change the calculated speed (e.g., longer distance means higher speed).","code":"C"}],"finalAnswers":[],"generatedAt":"2026-05-07T01:54:16.909Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"compare_routes","label":"Compare the route distances","steps":[{"type":"text","order":1,"title":"Allow for different distances","content":"Part (a) assumes both people travelled the same distance. Different roads could make Declan’s route longer or shorter, so the speed calculated in part (a) might not apply.\n\n**[C1]** If different roads made Declan's distance longer, his average speed would be higher; if they made it shorter, his average speed would be lower, because his journey time is unchanged.","highlights":[{"text":"If Declan took different roads than Anthony","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:14:33.552Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"igcse_maths__oxford_aqa","summaries":[{"id":"9997bc80-5049-467e-b793-ab0a89c3d64b","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"6a2d446e-b801-4492-80c2-f4e80a5e90a3","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"e619325f-8748-4bc0-9523-342f56cd3136","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"28fb089d-a56b-44ea-b28b-bede3bd51229","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"4087bd63-6a20-4722-b157-1af0e6a28fec","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"97eb4a8a-3ab0-49c9-ac18-ede2acf47eac","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"2848076d-1618-46f0-a141-dd19beb71878","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"3c180a39-9936-4db4-98e6-8f653e73be6e","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"f1e4cd96-ef4b-4d2e-ae14-9141db088e33","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"a0f9de5a-7959-45c1-815f-cd976fad04e4","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"aaf72873-1306-4e0a-bc88-f152d52b0551","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"33e0eb02-9b2f-4070-8dd3-fdce70daa773","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"8ee7546a-ef18-4f79-9549-e6bcc5835222","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false}],"title":"Speed and Density","topicId":"95a9cc82-b016-400b-9611-d62d523a2ec2","topicSidebar":"$L3b","topicSlug":"grade-5-5-3-speed-and-density","topicTitle":"Speed and Density"}]}],"$L3c","$L3d"]}]

Speed and Density

Question 2

Speed and Density Questions

Speed and Density

Question 2

Speed and Density Questions