Mike six years old is twice as his brother How will be when he one and a half times brother?

Let M be Mike's current age and B be his brother's current age.

We know that Mike is six years old and twice his brother's age:

M = 6

M = 2B

Substituting M = 6 into M = 2B, we get:

6 = 2B

B = 6/2 = 3

So, Mike's brother is currently 3 years old.

We want to find out when Mike will be one and a half times his brother's age. Let x be the number of years from now. In x years:

Mike's age will be M + x = 6 + x

Brother's age will be B + x = 3 + x

We want to find x such that:

6 + x = 1.5 * (3 + x)

Now we solve for x:

6 + x = 4.5 + 1.5x

6 - 4.5 = 1.5x - x

1.5 = 0.5x

x = 1.5 / 0.5

x = 3

Therefore, in 3 years:

Mike will be 6 + 3 = 9 years old

His brother will be 3 + 3 = 6 years old

9 is 1.5 times 6 (9 = 1.5 * 6).

So Mike will be one and a half times his brother's age in $\boxed{3}$ years.