Answer
$1.5$ hours
Work Step by Step
Using $d=rt$ where $d$ is the distance, $r$ is the rate, and $t$ is the time, then the equation representing the first half of the travel is
$$\begin{aligned}
10&=12t_1
\\
t_1&=\frac{10}{12}
\\&=
\frac{5}{6}
.\end{aligned}$$
The equation representing the travel going back is
$$\begin{aligned}
10&=(12+3)t_2
\\
t_2&=\frac{10}{15}
\\&=
\frac{2}{3}
.\end{aligned}$$
The total time of the travel, $t$, is
$$\begin{aligned}
t&=t_1+t_2
\\&=
\frac{5}{6}+\frac{2}{3}
\\&=
\frac{5}{6}+\frac{4}{6}
\\&=
\frac{9}{6}
\\&=
\frac{3}{2}
\\&=
1.5
.\end{aligned}$$Hence, the total travel time is $1.5$ hours.
