ShmoopTube

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Here's your shmoop du jour...

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Two cars, starting at the same place, took different routes to the same destination.

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Their speeds with respect to time are given by the graph shown below. 

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According to the graph, when do the cars achieve their greatest difference in speeds?

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And here are the potential answers:

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Can we read a line graph?

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The question is asking for a DIFFERENCE in speed so

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we know there’s a big fat subtraction problem coming.

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We just have to know what we’re subtracting from what.

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And we’re on the hunt for the biggest difference here… so where are the lines furthest apart?

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…let’s just use the potential answer set to figure out the differences.

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A says: After 5 minutes.

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Well, if this is after 20 minutes… and half way back to t minus zero is here – that’ll

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be the 10 minute mark and half way again puts us here at the 5 minute mark…

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So… ok… we put our ruler here and draw a line straight up…

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…and we intersect the blue line at about the 15 mile per hour mark and then don’t

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hit green line car 1 until the 40 minute mark.

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A difference of 25 miles an hour. OK, how about B? After 10 minutes, blue is

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at about 37 miles an hour and green is about 50 miles an hour… so just about 13 miles

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an hour difference there. A is still winning. C. Well, after 20 minutes they are about the

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same speed so C doesn’t have a prayer. Let’s try D. Green is about 62 and blue

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is about 70 – slow and steady wins the race, we guess…

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…but we didn’t care WHO wins – all we care about for this problem is at what point

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there is the greatest distance between the two cars.

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It looks like the winner is answer A with 25 miles an hour difference after minute 5.

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