Question 893809
Many examples like this are requested.


The described problem can be generalized like this:
A vehicle starts traveling from city A towards city B. It maintains a speed of r miles per hour.
 Another vehicle starts the same trip k <b>hours</b> later going R miles per hour.
Where (a distance from city A) will the faster vehicle take over the slower one.
{{{0<r<R}}}, and {{{k>0}}}.


Let d be the distance where the late fast car reaches the early slow car.
t is unknown,
d is unknown.


_________________speed________time_______distance
EARLY SLOW________r___________t+k_________d
LATE FAST_________R____________t__________d


EQUATIONS
{{{r(t+k)=d}}} and {{{Rt=d}}};
Solve for t and d.


Simply equating the two formulas for d,
{{{r(t+k)=Rt}}}
{{{rt+rk=Rt}}}
{{{rt+rk-Rt=0}}}
{{{rt-Rt=-rk}}}
{{{t(r-R)=-rk}}}
{{{t=-rk/(r-R)}}} and then multiply by {{{(-1)/(-1)}}}
{{{highlight(t=rk/(R-r))}}}


Use this result for t in either of the original equations to find d.
{{{d=Rt}}}
{{{d=R(rk/(R-r))}}}
{{{highlight(d=(rRk)/(R-r))}}}, d, the distance completely in symbolic form.


Now you can simply substitute the values from the problem description for r, R, and k, and evaluate d.