2015 AMC 8

Complete problem set with solutions and individual problem pages

Problem 17 Hard

Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?

  • A.

    4

  • B.

    6

  • C.

    8

  • D.

    9

  • E.

    12

Answer:D

Solution 1

For starters, we identify d as distance and v as velocity (speed)

Writing the equation gives us: \frac{d}{v}=\frac{1}{3} and \frac{d}{v+18}=\frac{1}{5}.

This gives d=\frac{1}{5}v+3.6=\frac{1}{3}v, which gives v=27, which then gives d=\boxed{\textbf{(D)}~9}.

 

Solution 2

d = rt,d=frac{1}{3}times r = frac{1}{5}times (r + 18)$

\frac{r}{3} = \frac{r}{5} + \frac{18}{5}

10r = 270 so r = 27, plug into the first one and it's \boxed{\textbf{(D)}~9} miles to school.

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