Tyrone leaves city A on a moped traveling toward city B at 19 miles per hour. At the same time, Tina leaves city B on a bicycle traveling toward city A at 15 miles per hour. The distance between the two cities is 119 miles. How long will it take before Tyrone and Tina meet?

Lets establish two equations, one for Tyrone's and other for Tina's position on the route, which is 119 miles long. Lets take city A as the mile 0 and city B as mile 119.

So, when Tyrone stars he is in mile 0, and each hour that passes he moves 19 miles. If x is the number of hours since he left, we can say his position in terms of x is:

f(x)=19x

Tina starts in mile 119, each hour that passes she moves 15 miles. For example, after 1 hour she will be at mile 119-15=104, in the next hour in mile 89 and so on, subtracting 15 miles each hour. So, here position can be:

g(x) = 119 - 15x

As we want them to meet, it means their position is the same, being both functions equal for some x:

f(x) = g(x)

19x = 119 - 15x

Summing 15x in both sides:

19x + 15x = 119

34x = 119

Dividing both sides by 34:

x = 119/34 = 3.5

So, they meet after 3.5 hours.