Answer
120 miles
Work Step by Step
The total time of the trip was $4{2\over5}$ hours, so
$t_{1}+t_{2}=4{2\over5}$, where $t_{1}$ is the time Mary took to go to Belleville and $t_{2}$ is the time she took to go back.
Knowing that $t={d\over v}$, which is derived from $v={d\over t}$, where $t$ is time, $d$ is distance, and $v$ is speed, we can re-write the equation above.
${d\over v_{1}}+{d\over v_{2}}=4{2\over5}$
$d$ is the distance from one city to another. Now we put in the speeds driven into the equation:
${d\over 50}+{d\over 60}=4{2\over5}$
All that is left is to solve for $d$ which can be done by finding the least common denominator so we can add them up.
${6\over 6}\cdot {d\over 50}+{5\over 5}\cdot{d\over 60}=4{2\over5}$
${6d\over 300}+{5d\over 300}=4{2\over5}$
${11d\over 300}=4{2\over5}$
${d}={4{2\over5}(300) \over 11}$
$d=120$ miles
