Swapping places!

$\text {The hour hand moves }2\pi \text{ radian in} \text{ 12 hours}\\ \text {The minute hand moves }2\pi \text{ radian in} \text{ 1 hour}\\ \text{Let `t' be the time taken in hours for Tom to get to school,in time t both the hands combined have moved } 2\pi \text{ radians}\\ \begin{aligned}\implies \dfrac{2\pi}{12}\times t+\dfrac{2\pi}{1}\times t&=2{\pi} \\ \implies \dfrac{t}{12}+t&=1\\ \implies t&=\color{#EC7300}\boxed{\color{#333333}\dfrac{12}{13}} \color{#333333} \text{ hours}\end{aligned}$

Let when Tom started from home, the minute hand of the clock made an angle x degrees with the hour hand, while the later made an angle y with the 1-hr mark. Then (360-x)/12=x or x=360/13. (30+x+y)/12=y or y=(30+x)/11=750/143. Therefore the minute hand made an angle of (9000/143) degrees with the 12-hr mark, and hence Tom started for school at 1hr (1500/143) min. When he reached school, the hands of the clock swapped. Therefore the time was then 2 hr (840/143) min, and hence he took (132/143) or (12/13) hour to reach the school.