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?

3.5 hours

Step-by-step explanation:

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.