This problem should be quite simple but I am having a hard time getting to the solution...
Imagine that I have the following path:
|--------|-----O--------|
A B C
Where O represents a car. Let's say that the Car is now 60% through the path A-C.
Knowing that B is 40% (regarding A-C), what is the distance (in %) covered on the path B-C?
On
Imagine the percentages are distances. A to C is $100\%$, so imagine that it's $100m$ (metres) in distance. A to B is $40\%$ of the distance, so call it $40m$, and so B to C would be $60m$.
If the car has covered $60\%$ of the distance, then the distance from A to the car is $60m$. The distance from A to B is $40m$, so the distance from B to the car is $60m - 40m$ = $20m$.
Then we can divide $20m$ by the distance from B to C to find the $\%$ distance covered from B to C. $20 \div 60 = \frac{1}{3}$, which as a percentage is $33.\dot{3}\%$.
$z$ the position of the car through A-C. The targeted percentage is : $\frac{z - B}{C-B}$ Why ? Because it's linear and you know that being at B is $0$ and being at C is $1$. If z stand for the percentage, then $C = 1$ and that is the same formula.