Question 967694
THE FIFTH-GRADER MENTAL MATH SOLUTION:
If 3 fourths (3/4) is 120 km,
then 1 fourth (1/4) is 120 km divided by 3, which is 40 km.
If 40 km is 1/4 of the trip,
then the entire trip is 4 times that:
4 times 40 km, which is 160 km.
 
THE FANCY EQUATION ALGEBRA WAY:
{{{x}}}= total trip distance in km.
{{{(3/4)x}}}= 3/4 of the total trip distance.
So, {{{(3/4)x=120}}} is our equation.
Solving:
{{{(3/4)x=120}}} 
Dividing both sides by {{{3/4}}} , (which, as you know,
is the same as multiplying by the reciprocal fraction, {{{4/3}}} )
we get
{{{(3/4)x/(3/4)=120/(3/4)}}} <---> {{{(4/3)(3/4)x=(4/3)*120}}}
{{{x=4*120/3}}} --> {{{x=4*40}}} -->{{{highlight(x=160)}}}