Question 909061
You can think of this as one train 
standing still and the other moving
at the sum of their speeds.
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Let {{{ s }}} = the speed of the slower train
{{{ s + 20 }}} = the speed of the faster train
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{{{ 371 = ( s + s + 20 )*3.5 }}}
{{{ 371 = ( 2s + 20 )*3.5 }}}
{{{ 371 = 7s + 70 }}}
{{{ 7s = 301 }}}
{{{ s = 43 }}}
{{{ s + 20 = 63 }}}
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The slower train's speed is 43 mi/hr
The faster train's speed is 63 mi/hr
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check:
Slower train:
{{{ d[1] = 43*3.5 }}}
{{{ d[1] = 150.5 }}}
Faster train:
{{{ d[2] = 63*3.5 }}}
{{{ d[2] = 220.5 }}}
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{{{ d[1] + d[2] = 150.5 + 220.5 }}}
{{{ d[1] + d[2] = 371 }}}
OK