Answer
$45$ miles per hour or $75$ miles per hour
Work Step by Step
Ricardo wants to get $20$ mile per gallon during his trip. We therefore substitute $20$ for $m$ and solve for $s$. \begin{aligned}
m(s) &= -\frac{1}{3} \lvert s-60\rvert+25\\
20&= -\frac{1}{3} \lvert s-60\rvert+25\\
(-3)\cdot 20&=(-3)\cdot -\frac{1}{3} \lvert s-60\rvert+(-3)\cdot 25\\
-60&= \lvert s-60\rvert-75\\
75-60&= \lvert s-60\rvert\\
15&= \lvert s-60\rvert.
\end{aligned} Rewrite into two equations and solve. \begin{aligned}
s-60&= 15\\
s& = 15+60\\
& = 75
\end{aligned} or \begin{aligned}
& s-60= -15\\
& = -15+60\\
& = 45.
\end{aligned} Now, check the solution. \begin{aligned}
m(75) &= -\frac{1}{3} \lvert 75-60\rvert+25\\
& = -\frac{1}{3} \lvert 15\rvert+25\\
& = -\frac{1}{3}\cdot 15+25\\
& = -5+25\\
& = 20
\end{aligned} and \begin{aligned}
m(45) &= -\frac{1}{3} \lvert 45-60\rvert+25\\
& = -\frac{1}{3} \lvert -15\rvert+25\\
& = -\frac{1}{3}\cdot 15+25\\
& = -5+25\\
& = 20.
\end{aligned} Hence, Ricardo must drive at $45$ miles per hour or at $75$ miles per hour to achieve a $20$ miles per gallons during his journey.
