// Numbas version: exam_results_page_options
{"name": "Use speed and distance to calculate time ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.</p>\n<p>Small, simple question.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["kilometres", "speed"], "type": "question", "rulesets": {}, "extensions": [], "variable_groups": [], "statement": "<p>At a greyhound race, a fake rabbit moves around the inside of the track to motivate the dogs to run.</p>\n<p>The track is&nbsp;$\\var{kilometres}$km long and the rabbit moves at a&nbsp;constant speed of $\\var{speed}$m/s.</p>", "name": "Use speed and distance to calculate time ", "advice": "<p>We are told that the track&nbsp;is $\\var{kilometres}$km long and that the speed of the rabbit is $\\var{speed}$m/s (metres per second).</p>\n<p>Most people remember the relationship between speed, distance and time with the formula</p>\n<p>\\[\\text{Average speed} = \\frac{\\text{Distance travelled}}{\\text{Total time taken}}.\\]</p>\n<p>We&nbsp;can rearrange the&nbsp;formula for&nbsp;average speed to give us&nbsp;the formula for the time taken:&nbsp;</p>\n<p>\\[\\text{Total time taken} = \\displaystyle\\frac{\\text{Distance travelled}}{\\text{Average speed}}.\\]</p>\n<p>Firstly, we must convert the units of the length of the race from kilometres to metres. We know that $1\\text{km} = 1000\\text{m}$, therefore</p>\n<p>\\begin{align}<br/>\\var{kilometres}\\text{km} &amp;= (\\var{kilometres} \\times 1000)\\text{m}\\\\<br/>&amp;= \\var{{kilometres}*1000}\\text{m}.<br/>\\end{align}</p>\n<p>Therefore, the time taken for the rabbit to finish one lap is</p>\n<p><span data-jme-visible=\"({kilometres}*1000)/{speed} = precround(({kilometres}*1000)/{speed},0)\">\\[\\displaystyle\\frac{\\var{{kilometres}*1000}}{\\var{speed}} = \\var{({kilometres}*1000)/{speed}} \\;&nbsp;\\text{seconds}.\\]</span></p>\n<p><span data-jme-visible=\"({kilometres}*1000)/{speed} &lt;&gt; precround(({kilometres}*1000)/{speed},0)\">\\[ \\begin{align} \\displaystyle\\frac{\\var{{kilometres}*1000}}{\\var{speed}} &amp;= \\var{({kilometres}*1000)/{speed}} \\; \\text{seconds}\\\\ &amp;= \\var{dpformat(({kilometres}*1000)/{speed}, 0)} \\;&nbsp;\\text{seconds} \\; (\\text{to the nearest second}).&nbsp;&nbsp;\\end{align}\\]</span></p>", "parts": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "stepsPenalty": 0, "steps": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "information", "showCorrectAnswer": true, "prompt": "<p>Speed, distance and time are related by the equation</p>\n<p>\\[\\text{Average speed} = \\frac{\\text{Distance travelled}}{\\text{Total time taken}}.\\]</p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0}], "prompt": "<p>Calculate the time taken for the rabbit to&nbsp;complete a circuit of the track.</p>\n<p>[[0]] seconds &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><small>Round your answer to the nearest second</small></em>.</p>", "gaps": [{"correctAnswerFraction": false, "variableReplacements": [], "precisionPartialCredit": 0, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2", "precision": 0, "showFeedbackIcon": true, "precisionType": "dp", "minValue": "({kilometres}*1000)/{speed}", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "({kilometres}*1000)/{speed}", "mustBeReduced": false, "allowFractions": false, "strictPrecision": false, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showPrecisionHint": false, "precisionMessage": "<p>Round your answer to the nearest second.</p>"}], "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true}], "tags": ["compound measures", "Compound measures", "Compound units", "compound units", "Distance", "distance", "km", "metres per second", "speed", "taxonomy", "Time", "time"], "preamble": {"js": "", "css": ""}, "functions": {}, "variables": {"speed": {"description": "<p>Speed of the greyhound in metres per second.</p>", "group": "Ungrouped variables", "definition": "random(14..18)", "name": "speed", "templateType": "anything"}, "kilometres": {"description": "<p>Kilometres to be ran by the greyhound</p>", "group": "Ungrouped variables", "definition": "random(0.35..0.49 #0.01)", "name": "kilometres", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}