Question 265640
It looks like Sarah got a headstart of 2 hrs.
How far did she get in 2 hrs?
{{{d = 40*2}}}
{{{d = 80}}} mi
Now, if I had a stopwatch I'd start it so that
they are both heading towards eachother and will 
meet somewhere between the houses.
I'll write equations for both:
(1) {{{d[s] = r[s]*t}}}
(2) {{{d[j] = r[j]*t}}}
The time is the same for both because I'll 
stop the stopwatch when they meet.
The houses are 221 mi apart, but now Sarah and Jen
are {{{221 - 80 = 141}}} mi apart, so I know
{{{d[s] + d[j] = 141}}}
From (1) and (2) above,
{{{d[s]/r[s] = d[j]/r[j]}}}
{{{d[s]/40 = d[j]/54}}}
Multiply both sides by {{{40}}}
{{{d[s] = (40/54)*d[j]}}}
By substitution:
{{{(40/54)*d[j] + d[j] = 141}}}
{{{40d[j] + 54d[j] = 7614}}}
{{{94d[j] = 7614}}}
{{{d[j] = 81}}}
And, since
{{{d[s] + d[j] = 141}}}
{{{d[s] = 141 - 81}}}
{{{d[s] = 60}}}
Jen has to drive 81 mi and Sarah has to drive 60 mi
check answer:
(1) {{{d[s] = r[s]*t}}}
{{{60 = 40*t}}}
{{{t = 60/40}}}
{{{t = 3/2}}} hr 
and
(2) {{{d[j] = r[j]*t}}}
{{{81 = 54*t}}}
{{{t = 81/54}}}
{{{t = 3/2}}} hr
The times are the same -OK