Question 205730
 
I will write 2 equations, 1 for the bus and 1 for the train
{{{d[b] = r[b]*t[b]}}}
and
{{{d[t] = r[t]*t[t]}}}
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given:
{{{r[b] = 50}}} mi/hr
{{{r[t] = 40}}} mi/hr
{{{t[t] = t[b] + 1}}}
{{{d[b] = d[t]}}} (I'll call them both {{{d}}})
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{{{d = 50*t[b]}}}
{{{d = 40*(t[b] + 1)}}}
{{{d = 40t[b] + 40}}}
I'll subtract these equations
{{{d = 50t[b]}}}
{{{-d = -40t[b] - 40}}}
{{{0 = 10t[b] - 40}}}
{{{10t[b] = 40}}}
{{{t[b] = 4}}} hr
Now I'll solve for {{{d}}}
{{{d = 50t[b]}}}
{{{d = 50*4}}}
{{{d = 200}}} mi
The town is 200 mi from where they started
check answer:
{{{d = 40t[b] + 40}}}
{{{200 = 40*4 + 40}}}
{{{200 = 160 + 40}}}
{{{200 = 200}}}
and
{{{t[t] =t[b] + 1}}}
{{{t[t] = 4 + 1}}}
{{{t[t] = 5}}} hr
{{{d = 40t[t]}}} 
{{{200 = 40*5}}}
{{{200 = 200}}}
OK