Question 96972
From your equation, it appears that you assumed that the two segments were the same distance, but there is nothing in the problem to support this assumption.
So, back to basics:
{{{d[1] = r[1]t[1]}}} and...
{{{d[2] = r[2]t[2]}}}
We know that:
{{{r[1] = 10}}} and...
{{{r[2] = 25}}}
{{{t[1] = t[2] + 2}}} and we also know that:
{{{d[1]+d[2] = 90}}} So we can write:
{{{d[1] = 10t[1]}}}
{{{d[2] = 25t[2]}}} aagh...to many variables! Let's replace {{{t[1]}}} with {{{t[2]+2}}} and replace {{{d[2]}}} with {{{90-d[1]}}}, so now we have:
{{{d[1] = 10(t[2]+2)}}} and
{{{90-d[1] = 25t[2]}}} Solve this for {{{d[1]}}}
{{{d[1] = 90-25t[2]}}}...but, of course, {{{d[1] = d[1]}}}, so...
{{{10(t[2]+2) = 90-25t[2]}}} Good, now we have one variable {{{t[2]}}}, so let's solve for it.
{{{10t[2]+20 = 90-25t[2]}}}
{{{35t[2]+20 = 90}}}
{{{35t[2] = 70}}} and...
{{{t[2] = 2}}}hrs. Now we can find {{{d[1]}}} and {{{d[2]}}}
{{{d[1] = 10(t[2]+2)}}}
{{{d[1] = 10(2+2)}}}
{{{d[1] = 40}}}km and...
{{{d[2] = 90-d[1]}}}
{{{d[2] = 90-40}}}
{{{d[2] = 50}}}km

Check:
Total distance is {{{d[1]+d[2] = 40+50}}} = 90km