VTMO 2015 — Grade 9 — semifinal Question 18

An drives at $55 \frac{\,\mathrm{km}}{h}$ for an integer number of hours. The odometer changes from $abc$ to cba, with $a \ge 1$ and $a + b + c \le 7$. Find a $^{2} + b^{2} + c^{2}$.