Let x be the number of minutes of calls.
For the first plan, the cost is 0.16x.
For the second plan, the cost is 29 + 0.12x.
Setting the costs equal to each other, we get 0.16x = 29 + 0.12x.
Subtracting 0.12x from both sides, we get 0.04x = 29.
Dividing both sides by 0.04, we get x = 725.
Thus, the costs of the two plans will be equal for 725 minutes of calls. Answer: \boxed{725}.