Question 110959
{{{t[a] + t[b] = t}}}
{{{d[a]/r[a] + d[b] /r[b] = t}}}
{{{d[b] = 150 - d[a]}}}
I put all the times in minutes and rates in terms
of km/min. 2 hrs 40 min = 160 min
{{{d[a] / (45/60) + (150 - d[a]) / (75/60) = 160}}}
{{{d[a] / (3/4) + (150 - d[a]) / (5/4) = 160}}}
{{{4*d[a] / 3 + 4*(150 - d[a]) / 5 = 160}}}
{{{5*4*d[a] + 3*4*(150 - d[a]) = 3*5*160}}}
{{{20*d[a] + 1800 - 12*d[a] = 2400}}}
{{{8*d[a] = 600}}}
{{{d[a] = 75}}}km answer
and
{{{d[b] = 150 - d[a]}}} 
{{{d[b] = 75}}}km answer
 She drove 75 km both parts of trip