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Calculus
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Nick and Tom are racing home. Nick starts on 78th street and runs uptown at a rate of 2 blocks per minute, and Tom runs downtown from 168th street at 3 blocks per minute. On what street will they meet? 

Oct 27th, 2015

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Number of blocks between Nick and Tom = 168 - 78 = 90

Let x be the number of blocks that Nick would have covered when he meets Tom.

So Tom would have covered 90 - x blocks by the time he meets Nick.


Nick's speed = 2 blocks per minute

Tom's speed = 3 blocks per minute


We know that 


or



So both of them would have run for t minutes before meeting. 

For Nick

 ---(1)


For Tom

 ---(2)


The LHS of equations (1) and (2) are equal. So their RHS must also be equal.



So Nick would have covered 36 blocks when he meets up with Tom.

Hence the street at which Nick and Tom meet = 78 + 36 = 114th street

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Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 27th, 2015

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