2010 AMC 10B Problems/Problem 10

We know that $d = vt$

Since we know that she drove both when it was raining and when it was not and that her total distance traveled is $16$ miles.

We also know that she drove a total of $40$ minutes which is $\dfrac{2}{3}$ of an hour.

We get the following system of equations, where $x$ is the time traveled when it was not raining and $y$ is the time traveled when it was raining:

$\left\{\begin{array}{ccc} 30x + 20y & = & 16 \\x + y & = & \dfrac{2}{3} \end{array} \right.$

Solving the above equations by multiplying the second equation by 30 and subtracting the second equation from the first we get:

$-10y = -4 \Leftrightarrow y = \dfrac{2}{5}$

We know now that the time traveled in rain was $\dfrac{2}{5}$ of an hour, which is $\dfrac{2}{5}*60 = 24$ minutes

So, our answer is:

$\boxed{\mathrm{(C)}= 24}$

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