Need a little help with a simple rate of change problem.

Any help would be greatly appreciated...Thanks!

Suppose L = 780 + 2t and C = 12 + 8t represent the population (in thousands) of two cities. In how many years will city L have twice as many inhabitants as city C.

Assume that t = 0 initially.

The equation asks when L is twice C. So when does L = 2C?

L = 2 C
780 + 2t = 24 + 16t
780 - 14t = 24
756 - 14t = 0
756 = 14t

t = 756 / 14
t = 54 years

You're looking for L = 2C

780 + 2t = 2*(12 + 8t)
t = 54 years

But that's just Algebra, you don't really need Calculus for this one.