Question 411735
Let {{{v}}} = velocity of train A
{{{v + 20}}} = velocity of train B
Let {{{t}}} = time for train A
{{{t - .5}}} = time for train B
{{{d[A] = d[B]}}}
write 2 equations: 1 for train A,  1 for train B
A:
{{{200 = v*t}}}
B:
{{{200 = (v + 20)*(t - .5)}}}
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{{{200 = (v + 20)*(t - .5)}}}
{{{200 = vt + 20t - .5v - 10}}}
By substitution:
{{{200 = 200 + 20t - .5v - 10}}}
{{{.5v = 20t - 10}}}
{{{v = 40t - 20}}}
By substitution:
{{{200/t = 40t - 20}}}
{{{200 = 40t^2 - 20t}}}
{{{2t^2 - t - 10 = 0}}}
Use quadratic formula:
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{a = 2}}}
{{{b = -1}}}
{{{c = -10}}}
{{{t = (-(-1) +- sqrt( (-1)^2-4*2*(-10) ))/(2*2) }}} 
{{{t = ( 1 +- sqrt( 1 + 80 ))/4 }}} 
{{{t = ( 1 + 9)/4 }}} (can't use the negative root)
{{{t = 5/2}}} 
It takes train A 2.5 hours to go 200 mi
and
{{{200 = v*t}}}
{{{v = 200/2.5}}}
{{{v = 80}}}
For train B:
{{{200 = (v + 20)*(t - .5)}}}
{{{525 = (80 + 20)*t[B]}}}
{{{t[B] = 525/100}}
{{{t[B] = 5.25}}} hrs
It takes train B 5.25 hrs to go 525 mi