Let's start by setting up an equation to represent the situation:
59 + 57x = 15 + 79x
where x is the number of months it will take for both Thomas and Christian to have the same amount of money in their accounts.
Simplifying this equation, we get:
64x = 44
Dividing both sides by 64, we get:
x = 0.6875
So it will take approximately 0.6875 months for Thomas and Christian to have the same amount of money in their accounts. However, since time is measured in months, we cannot have a fraction of a month. Therefore, we round up the result to the nearest whole month and conclude that it will take 1 month for both Thomas and Christian to have the same amount of money in their accounts.