Question 339383
Write an equation for both men:
{{{d[A] = r[A]*t[A]}}}
and
{{{d[B] = r[B]*t[B]}}}
given:
{{{d[A] + d[B] = 19}}}
{{{t[A] = 2.5}}}
{{{t[B] = 2}}}
{{{r[A] = r[B] - .5}}}
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I can rewrite the equations of motion
{{{d[A] = r[A]*2.5}}}
and
{{{19 - d[A] = (r[A] + .5)*2}}}
{{{-d[A] = -19 + 2r[A] + 1}}}
{{{d[A] = 18 - 2r[A]}}}
and, since both are equal to {{{d[A]}}}
{{{2.5r[A] = 18 - 2r[A]}}}
{{{4.5r[A] = 18}}}
{{{r[A] = 4}}}
{{{r[B] = r[A] + .5}}}
{{{r[B] = 4.5}}}
The 1st man's rate is 4 mi/hr
The 2nd man's rate is 4.5 mi/hr
check:
{{{d[A] = r[A]*2.5}}}
{{{d[A] = 4*2.5}}}
{{{d[A] = 10}}} mi
and
{{{d[B] = r[B]*2}}}
{{{d[B] = 4.5*2}}}
{{{d[B] = 9}}}
{{{d[A] + d[B] = 19}}}
OK