China Mathematical Competition

Every day at a railway station, there is just one train arriving between $8:00$ am and $9:00$ am and between $9:00$ am and $10:00$ am, respectively. The arrival times and their probabilities for the two trains are shown in the following table:

Arrival time	Train A	$8:10$	$8:30$	$8:50$
Train B		$9:10$	$9:30$	$9:50$
Probability		$\frac{1}{6}$	$\frac{1}{2}$	$\frac{1}{3}$

Suppose that these random events are independent of each other. Now, a traveler comes into the station at $8:20$. Then the mathematical expectation of his waiting time is ______ (round to minute).