Question 5087
Of course the basic formula for this is D= RT.


Let t= time (in hours) required to arrive ON TIME

Change 1 minute early or late to {{{1/60}}} hour early or late.
{{{t+ 1/60}}} = time required to arrive a minute late at 40 mph.
{{{t - 1/60}}} = time required to arrive a minute early at 45 mph.

Distance is the same either way he arrives, so RT = RT
{{{40(t + 1/60) = 45 (t- 1/60) }}}


Use distributive property to remove the parentheses:
{{{40t + 40/60 = 45t - 45/60 }}}


Subtract 40t from each side:
{{{40t - 40t + 40/60 = 45t- 40t  - 45/60 }}}

{{{ 40/60 = 5t - 45/60 }}}


Add {{{45/60}}} to each side:
{{{40/60 + 45/60 = 5t - 45/60 +45/60}}}
{{{85/60 = 5t }}}


Divide both sides by 5:
{{{17/60 = t}}}hours.   (This means 17 minutes to arrive ON TIME!)


Distance = Rate * Time
(At 40)  {{{40*18/60}}}= 12 miles, arriving 1 minute late.
(At 45)  {{{45*16/60}}}= 12 miles, arriving 1 minute early.


Calculating distance both ways is a check!! 


R^2 at SCC