Question 703652
Let A = Speed of Train #1
Let B = Speed of Train #2
Equation 1: {{{A = B + 15}}} (One train is 15mph faster than the other)
Eqauation 2: {{{5A = 400 - 5B}}}
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Since we know the value of A, substitute (B+15) into equation 2 for A
Eqauation 2: {{{5A = 400 - 5B}}}
{{{5*(B + 15) = 400 - 5B}}}
Multiply the 5 through.
{{{5B + 75 = 400 - 5B}}}
Add 5B to both sides
{{{10B + 75 = 400}}}
Subtract 75 from both sides
{{{10B = 325}}}
Divide both sides by 10
{{{highlight(B = 32.5mph)}}}
Now plug 32.5 into equation 1 for B
Equation 1: {{{A = B + 15}}}
{{{A = (32.5) + 15}}}
{{{highlight(A = 47.5mph)}}}