Question 129835
Remember {{{d=rt}}}, so {{{t=d/r}}}.


Since we are interested in when and where they meet, their drive times must be equal.


Let's say that x is the distance Bob drives at 45 mph.  That means that the distance Joe drives at 65 mph is 243 - x.


Using {{{t=d/r}}}, Bob's drive time is {{{t=x/45}}}, and Joe's drive time is {{{t=(243-x)/65}}}.  But we already determined that these drive times are equal so we can say:


{{{x/45=(243-x)/65}}}


Cross multiply:
{{{65x=45(243-x)}}}
{{{65x=10935-45x}}}
{{{110x=10935}}}


From here on out, '=' means 'approximately equal to'

{{{x=99.41}}}, or Bob drove {{{99.41}}} miles to the meeting point.


Since we know that {{{t=d/r}}}, Bob's travel time must be {{{t=99.41/45}}} or {{{t=2.21}}} hours.  {{{.21}}} hours is {{{.21 * 60=12.6}}} minutes, and since they started at straight up noon, they must have met at 2:12.6 PM, and they met 99.41 miles from Bob's starting point.


Check:

Since they met at 99.41 miles from Bob's starting point, they must have met 243 - 99.41 = 143.59 miles from Joe's starting point.  If Joe travelled for 2.21 hours at 65 mph, he travelled {{{2.21 * 65 = 143.59}}} miles.  Answer checks.  (Actually, if you just plug in the numbers given, the calculator shows a bit of error, but if you do the arithmetic from the beginning on the calculator and never round off until the end, it all comes out correctly)