// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Q7 Ratio work times", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Ratio, working hours</p>\n<p>rebelmaths</p>"}, "tags": [], "name": "Simon's copy of Q7 Ratio work times", "statement": "", "variables": {"place": {"templateType": "anything", "description": "", "name": "place", "definition": "random('shop','business','factory')", "group": "Ungrouped variables"}, "number2": {"templateType": "anything", "description": "", "name": "number2", "definition": "random(3..18 except {number1})", "group": "Ungrouped variables"}, "time1": {"templateType": "anything", "description": "", "name": "time1", "definition": "random(5..20 except {number1} except {number2})", "group": "Ungrouped variables"}, "worker3": {"templateType": "anything", "description": "", "name": "worker3", "definition": "{worker2} * worker[2]", "group": "Ungrouped variables"}, "timeword1": {"templateType": "anything", "description": "", "name": "timeword1", "definition": "random(['hours','days'])", "group": "Ungrouped variables"}, "worker1": {"templateType": "anything", "description": "", "name": "worker1", "definition": "worker[0] * worker[1]", "group": "Ungrouped variables"}, "ans11": {"templateType": "anything", "description": "", "name": "ans11", "definition": "({worker3}/worker[2]) + {subvalue} + {worker3}", "group": "Ungrouped variables"}, "timeword2": {"templateType": "anything", "description": "", "name": "timeword2", "definition": "random(['hours','days'] except {timeword1})", "group": "Ungrouped variables"}, "number1": {"templateType": "anything", "description": "", "name": "number1", "definition": "random(5..15)", "group": "Ungrouped variables"}, "time2": {"templateType": "anything", "description": "", "name": "time2", "definition": "random(5..10#0.5 except {number1} except {number1} except {time1})", "group": "Ungrouped variables"}, "ans1": {"templateType": "anything", "description": "", "name": "ans1", "definition": "({number1}*{time1})/{number2}", "group": "Ungrouped variables"}, "ans3": {"templateType": "anything", "description": "", "name": "ans3", "definition": "({number2}*{time1}*{time2})/{number3}", "group": "Ungrouped variables"}, "worker2": {"templateType": "anything", "description": "", "name": "worker2", "definition": "{worker1} * worker[2]", "group": "Ungrouped variables"}, "subvalue": {"templateType": "anything", "description": "", "name": "subvalue", "definition": "(({worker3}/worker[2])/worker[1])", "group": "Ungrouped variables"}, "worker": {"templateType": "anything", "description": "", "name": "worker", "definition": "shuffle(5..12)[0..3]", "group": "Ungrouped variables"}, "ans2": {"templateType": "anything", "description": "", "name": "ans2", "definition": "({number2}*{time1}*{time2})/{number1}", "group": "Ungrouped variables"}, "number3": {"templateType": "anything", "description": "", "name": "number3", "definition": "random(3..18 except {number1} except {number2})", "group": "Ungrouped variables"}}, "variable_groups": [], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "functions": {"": {"type": "number", "language": "jme", "parameters": [], "definition": ""}}, "advice": "<p><strong>(a)</strong><em><br/></em></p>\n<p>Unskilled workers: $\\var{worker3}$</p>\n<p>Skilled workers: $\\frac{\\var{worker3}}{\\var{worker[2]}} = \\var{worker2}$</p>\n<p>Foremen: $\\frac{\\var{worker2}}{\\var{worker[1]}} = \\var{subvalue}$</p>\n<p>Total: $\\var{worker3} + \\var{worker2} + \\var{subvalue} = \\var{ans11}$</p>\n<p><em></em></p>\n<p><strong>(b)</strong></p>\n<p>If it takes $\\var{number1}$ people $\\var{time1}$ hours, then the job takes a total of&nbsp;$\\var{number1}&nbsp;\\times \\var{time1}= \\var{number1*time1}$ man hours.</p>\n<p>Dividing the total man hours by the number of people gives&nbsp;$\\frac{\\var{number1*time1}}{\\var{number2}} = \\var{precround(ans1,2)}$</p>\n<p></p>\n<p><strong>(c)</strong><em><br/></em></p>\n<p>The job takes a total of&nbsp;$\\var{number2}&nbsp;\\times \\var{time1} \\times \\var{time2}= \\var{number2*time1*time2}$ man hours.</p>\n<p></p>\n<p>(i) $\\frac{\\var{number2*time1*time2}}{\\var{number2}} = \\var{precround(ans2,2)}$</p>\n<p>(ii) $\\frac{\\var{number2*time1*time2}}{\\var{number3}} = \\var{precround(ans3,2)}$</p>", "parts": [{"variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "<p>A $\\var{place}$ employs $\\var{worker3}$ unskilled workers. They also employ one skilled worker for every $\\var{worker[2]}$ unskilled workers&nbsp;and one foreman for every $\\var{worker[1]}$ skilled workers. How many people are employed in this $\\var{place}$?</p>\n<p>[[0]]</p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "gaps": [{"maxValue": "{ans11}", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans11}", "allowFractions": false, "precision": "0", "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReduced": false, "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false, "mustBeReducedPC": 0, "precisionType": "dp", "strictPrecision": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "customMarkingAlgorithm": ""}], "sortAnswers": false, "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "<p>If $\\var{number1}$ people can complete a task in $\\var{time1}$ hours, how long would it take $\\var{number2}$ people to complete the same task, assuming the work rate remains constant?</p>\n<p>[[0]]hours</p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "gaps": [{"maxValue": "{ans1}", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans1}", "allowFractions": false, "precision": "2", "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReduced": false, "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": true, "mustBeReducedPC": 0, "precisionType": "dp", "strictPrecision": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "customMarkingAlgorithm": ""}], "stepsPenalty": 0, "sortAnswers": false, "type": "gapfill", "showFeedbackIcon": true, "steps": [{"variableReplacements": [], "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>It takes $\\var{number1} \\times \\var{time1}$ man hours to complete the task. Divide that by&nbsp;$\\var{number2}$ to find out how long it takes now.</p>", "marks": 0, "extendBaseMarkingAlgorithm": true, "type": "information", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "customMarkingAlgorithm": ""}], "customMarkingAlgorithm": ""}, {"variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "<p>It takes $\\var{number2}$ people $\\var{time1}$ days&nbsp;to do a job, working for $\\var{time2}$ hours per day. How many hours would it take:</p>\n<p>i) $\\var{number1}$ people to do the same job?&nbsp;</p>\n<p>[[0]]hours</p>\n<p>ii) $\\var{number3}$ people to do the same job?&nbsp;</p>\n<p>[[1]]hours</p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "gaps": [{"maxValue": "{ans2}", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans2}", "allowFractions": false, "precision": "2", "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReduced": false, "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": true, "mustBeReducedPC": 0, "precisionType": "dp", "strictPrecision": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "customMarkingAlgorithm": ""}, {"maxValue": "{ans3}", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans3}", "allowFractions": false, "precision": "2", "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReduced": false, "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": true, "mustBeReducedPC": 0, "precisionType": "dp", "strictPrecision": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "customMarkingAlgorithm": ""}], "sortAnswers": false, "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "preamble": {"css": "", "js": ""}, "extensions": [], "ungrouped_variables": ["number1", "number2", "time1", "time2", "timeword1", "timeword2", "ans1", "ans2", "number3", "ans3", "place", "worker", "worker2", "worker1", "worker3", "ans11", "subvalue"], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}