P, Q and R start from the same place X at (a) kmph, (a+b) kmph and (a+2b) kmph respectively.

Question

If Q starts p hours after P, how many hours after Q should R start, so that both Q and R overtake P at the same time?

Answer is pa/a+2b

Please solve this question in simplified and easy way

Answer 1

distance:
a t
(a+b)(t-p)
(a+2b)(t-p-x)

all the same :)
at =
at + bt -ap -bp
so
bt = ap + bp

at = at -ap -ax+2bt-2bp-2bx
(a+2b)x = -ap+2bt-2bp
x = (-ap+2bt-2bp)/(a+2b)
= (-ap+2ap +2bp-2bp)/(a+2b)
= ap/(a+2b)
whew !