At a distance of $48$ $m$, the front wheel of a car makes $10$ rotations more than the rear. If the circumference of the front wheel was $40$ $cm$ larger and of the rear wheel $40$ $cm$ smaller, at the same distance the two wheels would make the same number of rotations. Find the circumference of each wheel.
I tried to model a system of equations by using $C=2\pi r$ but I am not sure how. Can you give me a hint?
We can write that in equations:
$$4800cm=(N+10)C_{front} \quad 4800 cm=NC_{rear}$$
Where $N$ is the number of rotations and $C$ is the corresponding circumferences.
Then we have:
$$4800cm=N_x(C_{front}+40cm) \quad 4800cm=N_x(C_{rear}-40cm)$$
Where $N_x$ is the number of rotations now. From the last equation you get $C_{front}=C_{rear}-80cm$. You can do something similar with the first equation and you have a system of two equations with two unknowns.