51+ 0.13• miles driven (plan 1)
40+ 0.18• miles driven (plan 2)
If you drive 1 mile than plan 2 is better
51+ 0.13= 51.13
40+0.18= 40.18
The difference between the two initial fees is 51-40 = $11
With each mile driven plan 2 closes the difference gap by 0.18-0.13= $0.05
So after 11/0.05= 220 miles the better plan will be plan 1
If you drive 220 miles the plans cost is equal
51+ 0.13•220= $79.6
40+ 0.18•220= $79.6
Plan2 cheaper <220 miles < Plan1 cheaper