// Numbas version: exam_results_page_options {"name": "David's copy of 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": [{"preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "
Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.
\nSmall, simple question.
"}, "ungrouped_variables": ["kilometres", "speed"], "advice": "We are told that the track is $\\var{kilometres}$km long and that the speed of the rabbit is $\\var{speed}$m/s (metres per second).
\nMost people remember the relationship between speed, distance and time with the formula
\n\\[\\text{Average speed} = \\frac{\\text{Distance travelled}}{\\text{Total time taken}}.\\]
\nWe can rearrange the formula for average speed to give us the formula for the time taken:
\n\\[\\text{Total time taken} = \\displaystyle\\frac{\\text{Distance travelled}}{\\text{Average speed}}.\\]
\nFirstly, 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
\n\\begin{align}
\\var{kilometres}\\text{km} &= (\\var{kilometres} \\times 1000)\\text{m}\\\\
&= \\var{{kilometres}*1000}\\text{m}.
\\end{align}
Therefore, the time taken for the rabbit to finish one lap is
\n\\[\\displaystyle\\frac{\\var{{kilometres}*1000}}{\\var{speed}} = \\var{({kilometres}*1000)/{speed}} \\; \\text{seconds}.\\]
\n\\[ \\begin{align} \\displaystyle\\frac{\\var{{kilometres}*1000}}{\\var{speed}} &= \\var{({kilometres}*1000)/{speed}} \\; \\text{seconds}\\\\ &= \\var{dpformat(({kilometres}*1000)/{speed}, 0)} \\; \\text{seconds} \\; (\\text{to the nearest second}). \\end{align}\\]
", "extensions": [], "variable_groups": [], "variables": {"speed": {"group": "Ungrouped variables", "templateType": "anything", "description": "Speed of the greyhound in metres per second.
", "definition": "random(14..18)", "name": "speed"}, "kilometres": {"group": "Ungrouped variables", "templateType": "anything", "description": "Kilometres to be ran by the greyhound
", "definition": "random(0.35..0.49 #0.01)", "name": "kilometres"}}, "rulesets": {}, "name": "David's copy of Use speed and distance to calculate time", "parts": [{"marks": 0, "stepsPenalty": 0, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "steps": [{"marks": 0, "type": "information", "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "prompt": "Speed, distance and time are related by the equation
\n\\[\\text{Average speed} = \\frac{\\text{Distance travelled}}{\\text{Total time taken}}.\\]
"}], "prompt": "Calculate the time taken for the rabbit to complete a circuit of the track.
\n[[0]] seconds Round your answer to the nearest second.
", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"showPrecisionHint": false, "strictPrecision": false, "allowFractions": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "minValue": "({kilometres}*1000)/{speed}", "showFeedbackIcon": true, "precision": 0, "precisionType": "dp", "mustBeReducedPC": 0, "showCorrectAnswer": true, "marks": "2", "variableReplacements": [], "precisionPartialCredit": 0, "maxValue": "({kilometres}*1000)/{speed}", "mustBeReduced": false, "precisionMessage": "Round your answer to the nearest second.
", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain"}]}], "functions": {}, "statement": "At a greyhound race, a fake rabbit moves around the inside of the track to motivate the dogs to run.
\nThe track is $\\var{kilometres}$km long and the rabbit moves at a constant speed of $\\var{speed}$m/s.
", "tags": ["compound measures", "Compound measures", "Compound units", "compound units", "Distance", "distance", "km", "metres per second", "speed", "taxonomy", "Time", "time"], "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}, {"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": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}