Question 981814
This type of travel uniform rates problems is common.


r, speed of slow car
R, speed of fast car
k, how much time that slow car travels before fast car begins same direction from common departure location
t, travel time of the fast car
d, distance that both cars traveled to same point on the route


GIVEN VALUES FOR VARIABLES
{{{system(r=30,R=50,k=1,t=unknown,d=unknown)}}}



___________________speed____________time__________distance
SLOW-early__________r_______________t+k___________d
FAST-late___________R________________t____________d


Note again, both cars will reach the same distance d, and unknown variable; but we can still solve for the other unknown, t.


{{{system(r(t+k)=d,Rt=d)}}}


{{{r(t+k)=Rt}}}, because the two cars go the same distance when fast car overtakes slow car.


{{{rt+rk=Rt}}}


{{{rt+rk-Rt=0}}}


{{{rt-Rt+rk=0}}}


{{{(r-R)t+rk=0}}}


{{{(r-R)t=-rk}}}
You KNOW that {{{r-R}}} will be negative and that {{{-rk}}} is also negative so multiply left and right by  {{{-1}}}...


{{{(R-r)t=rk}}}


{{{highlight(t=(rk)/(R-r))}}}, time in hours for fast late car to overtake the slow early car.
Substitute the given values and evaluate t.