thinking outside of the box
posted by eva .
one taxi company charges 75 cents for the first quarter mile and 15 cents for each additional mile the competing taxi company charges 1.00 for the first quarter mile and 10 each additional mile what distance would produce the same fare for the two taxi companies?

The fare is the same when the distance x satisfies this equation:
0.75 + 0.15(x0.25) = 1.00 + 0.10(x0.25)
0.15x + 0.7125 = 0.10x + 0.9750
x = 5.25 miles
You could do this without algebra. After the first quarter mile, the second taxi costs 25 cents more. You need to go 5 more miles to make up the difference at 5 cents per mile.