First I think we should figure out the equation for both car have travel (km)

First Car:
Let assume
x is the total distancs for the first have travel in 15 minutes.
y is the total time that first car have travel (in minutes)
z is the travel speed of first car

So,
x = yz/60

Second Car:
Let assume
a is the total distancs for the first have trave (in km).
b is the total time that first car have travel (in minutes)
c is the travel speed of first car

So,

a = bc/60

Now, we can combine this 2 equation and calculate the time needed for the second car to catch up the first car.

i. x = yz/60
ii. a = bc/60

Since x = a,
Therefore,

[b]yz/60 = bc/60[b]
[b]yz = bc[b]
Our final answer is y,

y = bc/z

But because the first car have strat travel in 15 minutes early than the second car so, the final solution
should become:

Let assume t is the time that firt car have travel before the second car start travel.

y-t = bc/z

Now, we can fill in the variable with the respective value:
Let assume second car have travel 1 hour (60 minutes)
t = 15 minutes

y-15 = (60*100)/80
y = 75 minutes

As a result, I think the fastest and flexible solution is the following equation:

y = (bc/z) + t

Where:
b = Total time for second to catch up with first car.
y = Total time that first car have travel.
z = Travel speed for the first car.
c = Travel speed for the second car.
y = Total time for the first car have travel.

and you can create a GUI enable user to enter the respective value and let your program to calculate it.

Hope this can help you.