Question 302429
Let {{{s}}} = Smith's speed
Then {{{s + 5}}} = Jone's speed
Let {{{t}}} = Smith's time
Then {{{t + .5}}} = Jone's time
Write an equation for each one
For Smith:
{{{45 = s*t}}}
{{{t = 45/s}}}
For Jones:
{{{70 = (s + 5)*(t + .5)}}}
This is 2 equations and 2 unknowns, so it's solvable
{{{70 = s*t + 5t + .5s + 2.5}}}
by substitution:
{{{70 = 45 + 5t + .5s + 2.5}}}
by substitution again:
{{{25 = 5*(45/s) + .5s + 2.5}}}
{{{25 - 2.5 = 225/s + .5s}}}
Multiply both sides by {{{s}}}
{{{22.5s = 225 + .5s^2}}}
Multiply both sides by {{{10}}}
{{{225s = 2250 + 5s^2}}}
{{{5s^2 - 225s + 2250 = 0}}}
{{{s^2 - 45s + 450 = 0}}}
Use quadratic formula
{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = -45}}}
{{{c = 450}}}
{{{s = (-(-45) +- sqrt( (-45)^2-4*1*450 ))/(2*1) }}}
{{{s = (45 +- sqrt(2025 - 1800 ))/2 }}}
{{{s = (45 +- sqrt(225))/2 }}}
{{{s = (45 +- 15)/2 }}}
{{{s = 30}}}
{{{s = 15}}}
There's a choice of 2 answers. I'll try 
{{{s = 30}}}
{{{s + 5 = 35}}}
check:
{{{45 = s*t}}}
{{{t = 45/30}}}
{{{t = 1.5}}} hrs
and
{{{70 = (s + 5)*(t + .5)}}}
{{{70 = (30 + 5)*(t + .5)}}}
{{{t + .5 = 70/35}}}
{{{t = 2 - .5}}}
{{{t = 1.5}}} hrs
{{{t + .5 = 2}}} hrs
----------------------
also:
{{{s = 15}}}
{{{s + 5 = 20}}}
check:
{{{45 = s*t}}}
{{{t = 45/15}}}
{{{t = 3}}}
{{{70 = (s + 5)*(t + .5)}}}
{{{70 = (15 + 5)*(t + .5)}}}
{{{70/20 = t + .5}}}
{{{t = 3.5 - .5}}}
{{{t = 3}}} hrs
{{{t + .5 = 3.5}}} hrs
There are 2 possibilities:
(1)
Smith traveled 30 mi/hr
Jones traveled 35 mi/hr
(2)
Smith traveled 15 mi/hr
Jones traveled 20 mi/hr