2017 AMC 12A Problem 13

Problem 13 of 25IntermediateAlgebra

Driving at a constant speed, Sharon usually takes

180

minutes to drive from her house to her mother’s house. One day Sharon begins the drive at her usual speed, but after driving

\dfrac{1}{3}

of the way, she hits a bad snowstorm and reduces her speed by

20

miles per hour. This time the trip takes her a total of

276

minutes. How many miles is the drive from Sharon’s house to her mother’s house?

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Solution

Let the distance be

d

miles and the usual speed

r

mph. Since the usual trip is

3

hours,

d=3r.

The first

\dfrac{1}{3}

of the drive takes

\dfrac{1}{3}\cdot180=60

minutes at speed

r,

so the remaining

\dfrac{2}{3}

takes

276-60=216

minutes

=\dfrac{18}{5}

hours at speed

r-20.

That final portion covers

\dfrac{2}{3}d=2r

miles, so

2r=(r-20)\cdot\dfrac{18}{5}.

Solving gives

10r=18r-360,

r=45

and

d=3\cdot45=135.

Thus, the correct answer is B.