Question 203761
Let F = the time taken to finish the first half of the exam.
Let S = the time taken to finish the second half of the exam.
F+S = 1 hour or...
1) {{{F+S = 60}}} minutes. and...
2) {{{F = (2/3)*S}}} "...student finishes the first half of the exam (F) in {{{2/3}}} the time it takes to finish the second half of the exam {{{(2/3)*S}}}.
From this we can write the equation:
{{{F+S = 60}}} Substitute from equation 2) {{{F = (2/3)*S}}}
{{{((2/3)S)+S = 60}}} Add the S-terms on the left side.
{{{(5/3)S = 60}}} Multiply both sides by the multiplicative inverse of {{{5/3}}} which is {{{3/5}}}
{{{(5/3)(3/5)S = (3/5)(60)}}} Evaluate this.
{{{S = 36}}} so...
{{{F = (2/3)S}}}
{{{F = (2/3)(36)}}}
{{{highlight(F = 24)}}}minutes.