Question 227176
They will both be running for the same
amount of time. They just have different
starting points.
Let {{{t}}} = the amount of time they will 
be running in min
Each one has an equation.
Christina:
{{{d[c] = r[c]*t}}}
Brittany:
{{{d[b] = r[b]*t}}}
given:
{{{r[c] = 1/9}}} mi/min
{{{r[b] = 1/6}}} mi/min
{{{d[b] = d[c] + 1/3}}}
-----------------------
rewriting equations:
(1) {{{d[c] = (1/9)*t}}}
(2) {{{d[c] + 1/3 = (1/6)*t}}}
I have 2 equations and 2 unknowns, so it's solvable
(1) {{{d[c] = (1/9)*t}}}
{{{9d[c] = t}}}
and
(2) {{{d[c] + 1/3 = (1/6)*t}}}
{{{6d[c] + 2 = t}}}
Substitute (1) in (2)
{{{6d[c] + 2 = 9d[c]}}}
{{{3d[c] = 2}}}
{{{d[c] = 2/3}}} mi
Plugging back into (1)
 (1) {{{d[c] = (1/9)*t}}}
{{{2/3 = (1/9)*t}}}
{{{t = 9*(2/3)}}}
{{{t = 6}}} min
It will take Brittany 6 min to catch Christina
check:
(1) {{{d[c] = (1/9)*t}}}
{{{2/3 = (1/9)*6}}}
{{{2/3 = 6/9}}}
{{{2/3 = 2/3}}}
and
(2) {{{d[c] + 1/3 = (1/6)*t}}}
{{{2/3 + 1/3 = (1/6)*6}}}
{{{1 = 1}}}
OK