// 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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "

Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.

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Small, simple question.

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At a greyhound race, a fake rabbit moves around the inside of the track to motivate the dogs to run.

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The track is $\\var{kilometres}$km long and the rabbit moves at a constant speed of $\\var{speed}$m/s.

", "name": "Use speed and distance to calculate time ", "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).

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Most people remember the relationship between speed, distance and time with the formula

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\$\\text{Average speed} = \\frac{\\text{Distance travelled}}{\\text{Total time taken}}.\$

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We can rearrange the formula for average speed to give us the formula for the time taken:

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\$\\text{Total time taken} = \\displaystyle\\frac{\\text{Distance travelled}}{\\text{Average speed}}.\$

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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

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\\begin{align}
\\var{kilometres}\\text{km} &= (\\var{kilometres} \\times 1000)\\text{m}\\\\
&= \\var{{kilometres}*1000}\\text{m}.
\\end{align}

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Therefore, the time taken for the rabbit to finish one lap is

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\$\\displaystyle\\frac{\\var{{kilometres}*1000}}{\\var{speed}} = \\var{({kilometres}*1000)/{speed}} \\; \\text{seconds}.\$

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\\\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}\

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Speed, distance and time are related by the equation

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\$\\text{Average speed} = \\frac{\\text{Distance travelled}}{\\text{Total time taken}}.\$

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Calculate the time taken for the rabbit to complete a circuit of the track.

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