Question 235957
Since we are using two different time variables I think it is best to convert everything to one unit or the other.  I am going to convert everything into minutes.
1hour = 60min
{{{(40miles/1hour)*(1hour/60min) = ((0.6667*miles)/min)}}}
{{{(45miles/1hour)*(1hour/60min) = ((0.75*miles)/min)}}}
In these equations X = time & Y = distance.
Equation 1: {{{0.6667*(X+2) = Y}}}
The X+2 is the diffence in the arrival times.  1 minute ealry + 1minute late = 2 minutes.
Equation 2: {{{0.75*X = Y}}}
Since both equations equal Y, we can set these equations equal to each other.
{{{0.6667*(X+2) = 0.75*X}}} Simplify
{{{0.6667X + 1.3334 = 0.75X}}} Subtract 0.6667X from both sides
{{{1.3334 = 0.75X - 0.6667X}}} Factor out the X
{{{1.334 = X*(0.75-.06667)}}} Simplify
{{{1.334 = X*(0.0833)}}} Divide both sides by 0.08333
{{{highlight(16 = X)}}}  Now we know that the time traveled was 16 minutes
Plug 16 in for X into one of the given equations
Equation 2: {{{0.75*X = Y}}}
{{{0.75*(16) = Y}}}
{{{highlight(12 = Y)}}}
Equation 1: {{{0.6667*(X+2) = Y}}}
{{{0.6667*(16+2) = Y}}}
{{{0.6667*(18) = Y}}}
{{{highlight(12 = Y)}}}