Question 173668
a) call the time traveled by the van t
b.) time traveled by car call {{{t[2]}}} which equals t-3/4
c)
:

........rate........time.......distance
van......35...........t.........35t
car......50..........t-3/4......50t-75/2
:
so for
.................................van mi...........car mi
D(t)=D(1/2)............35/2.........0(they hadnt started driving yet)
.....D(1)......................35...........25/2
.....D(3/2).................105/2..........75/2
.....D(2).....................70..............125/2
.....D{{{highlight((5/2))}}}.............175/2.......175/2(at this point they are at the same spot)
:
if you were doing this by formulas
:
D=35t and D=50t-75/2...since the Distances are equal when the car catches up, this allows us to  set the equations equal to one another.
:
35t=50t-75/2..multiply each term by 2
:
70t=100t-75
:
-30t=-75
:
t=-75/-30=75/30=25/10={{{highlight(5/2)}}}