Question 7648
Let's call the total distance D. 1/4 of the distance would be {{{ (1/4)D }}}. The next 1/3 of the distance is {{{ (1/3)D }}}, and after both distances are covered, there are 5 miles to go. So, just add up the three distances and they all should equal D:


{{{ (1/4)D + (1/3)D + 5 = D }}} <---- You've got fractions to work with here, so hang on.


{{{ 5 = D - (1/4)D - (1/3)D }}} <---- We just moved the fractional terms to the other side so they could be combined since they are like terms.


The right side of the equation really is a task for you to compute {{{ 1 - 1/4 - 1/3 }}}. I trust that you know how to do that. That's actually equal to {{{ 12/12 - 3/12 - 4/12 }}} which brings you to {{{ 5/12 }}}. The right side of your equation would then be {{{ (5/12)D }}}


{{{ 5 = (5/12)D }}} <---- the 1 - 1/4 - 1/3, then multiplied by D


{{{ 5*(12/5) = D }}} <---- multiply both sides by the reciprocal of 5/12, which is 12/5


{{{ D = 12 }}} <---- the 5 in the numerator cancels with the 5 in the denominator. The trip was 12 miles total.