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Algebra and functions: world problem a'la shmoop

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Lance rode his bike to school pedaling at an average speed of 12 miles per hour. [Lance riding his bike to school]

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When he rode his bike back home at a leisurely pace of 10 miles per hour, it took him an

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extra 15 minutes.

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So..how far is his school from his home?

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And here are the potential answers…

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As you know, a full day of school can really sap your energy. [Tired boy sleeping after a exhausting day at school]

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So it’s no surprise that Lance is draggin’ a bit on the way home.

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This question is asking about the difference that those 2 miles an hour make… [Road leading from school to lance's home]

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…since they lost Lance an extra 15 minutes.

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Time that could have been well spent doing math homework. [Boy doing math homework]

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Okay, formula time.

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There's a basic equality here – since Lance is traveling the same distance both ways. [Lance travelling down a road from home to his school and riding back]

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It's just taking him a little longer on the way back home.

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Pick up the pace, boy…

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All right…so let’s call the 12 miles per hour average Lance took to get to school “12x”…

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…and the time it took him to get home “10x + 0.25”.

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The 10x represents his average speed on the way home…

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… and the “0.25” represents the extra quarter of an hour it takes him to pedal his [clock ticking by]

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way home.

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Because Lance is traveling an equal distance both times, we can say that 12x = 10x + 2.5.

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Take away 10x from both sides…

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And we get 2x = 2.5.

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Divide both sides by 2 and we have a value for our “x”…1.25 hours. [2x and 0.25 divided by 2]

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That’s nice and all… but we’re solving for distance. [Boy shrugging his shoulders at math equations]

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So we still have to multiply the time by Lance’s average speed.

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We take 1.25 hours multiplied by 12 miles per hour which gives us our final answer…15

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miles.

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Looks like the answer is option E – Lance has a 15 mile ride to and from school. [Lance cycles across the screen]

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Sheesh.

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We get tired driving our car for 15 miles… [Man falling asleep on his steering wheel]

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