Question 179739
To do this problem, you have to know what a 
relay race is. The runners runners run one 
at a time. One after the other.
For 1st runner
(1) {{{d[1] = r[1]*t[1]}}}
For 2nd runner
(2) {{{d[2] = r[2]*t[2]}}}
given:
{{{d[1] + d[2] = 6000}}}m
{{{d[2] = 6000 - d[1]}}}
{{{t[1] + t[2] = 18.5}}}min
{{{t[2] = 18.5 - t[1]}}}min
{{{r[1] = 300}}}m/min
{{{r[2] = 350}}}m/min
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Rewriting (1) and (2)
(1) {{{d[1] = 300t[1]}}}
(2) {{{6000 - d[1] = 350*(18.5 - t[1])}}}
This is 2 equations and 2 unknowns, so it's solvable
(1) {{{d[1] = 300*t[1]}}}
(2) {{{6000 - d[1] = 6475 - 350t[1]}}}
(2) {{{-d[1] = -350t[1] + 475}}}
Now add (1) and (2)
(2) {{{-d[1] = -350t[1] + 475}}}
(1) {{{d[1] = 300t[1]}}}
{{{0 = -50t[1] + 475}}}
{{{50t[1] = 475}}}
{{{t[1] = 9.5}}}min
And since
{{{t[2] = 18.5 - t[1]}}}min
{{{t[2] = 18.5 - 9.5}}}
{{{t[2] = 9}}}min
The 1st runner held the baton for 9.5 min, the 2nd for 9 min
check:
(1) {{{d[1] = 300*9.5}}}
{{{d[1] = 2850}}}
(2) {{{d[2] = 350*(18.5 - 9.5)}}}
{{{d[2] = 3150}}}
{{{d[1] + d[2] = 6000}}}m
{{{2850 + 3150 = 6000}}}
{{{6000 = 6000}}}OK