Question 273172
Write 2 equations:
Going to work:
{{{d = r[1]*t[1]}}}
Coming home from work:
{{{d = r[2]*t[2]}}}
---------------------
given:
{{{r[1] = 45}}} mi/hr
{{{r[2] = 30}}} mi/hr
{{{t[1] + t[2] = 1}}} hr
---------------------
{{{d = 45t[1]}}}
{{{d = 30t[2]}}}
then
{{{d/45 = t[1]}}}
{{{d/30 = t[2]}}}
Add the equations
{{{d*(1/45 + 1/30) = t[1] + t[2]}}}
{{{d = 1/(1/45 + 1/30)}}}
{{{d = 1/(2/90 + 3/90)}}}
{{{d = 1/(5/90)}}}
{{{d = 18}}} mi
Esther drove 18 mi to work 
check:
{{{d/45 = t[1]}}}
{{{t[1] = 18/45}}}
and
{{{d/30 = t[2]}}}
{{{t[2] = 18/30}}}
{{{t[1] + t[2] = 18/45 + 18/30}}}
{{{t[1] + t[2] = 18*(1/45 + 1/30)}}}
{{{t[1] + t[2] = 18*(2/90 + 3/90)}}}
{{{t[1] + t[2] = 18*(5/90)}}}
{{{t[1] + t[2] = 18*(1/18)}}}
{{{t[1] + t[2] = 1}}} hr
OK