##### Need help with Math homework

 Calculus Tutor: None Selected Time limit: 1 Day

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

$Speed=\frac{Distance}{Time}$

or

$Time=\frac{Distance}{Speed}$

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

For Nick

$t=\frac{x}{2}$ ---(1)

For Tom

$t=\frac{90-x}{3}$ ---(2)

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

$\\ \frac{x}{2}=\frac{90-x}{3}\\ \\ 3x=2(90-x)\\ \\ 3x=180-2x\\ \\ 3x+2x=180\\ \\ 5x=180\\ \\ x=\frac{180}{5}\\ \\ x=36$

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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Oct 27th, 2015

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Oct 27th, 2015
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Oct 27th, 2015
May 28th, 2017
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