We can use a proportion to solve the problem:
Let x be the number of minutes it would take Mika to eat 35 hot dogs
Then we can set up the proportion:
21 hot dogs / 6 minutes = 35 hot dogs / x minutes
To solve for x, we can cross-multiply:
21 hot dogs * x minutes = 6 minutes * 35 hot dogs
21x = 210
x = 10
Therefore, it would take Mika 10 minutes to eat 35 hot dogs if she can keep up the same pace.