Charles and Smith left a place abc at the same time and stated moving in the same direction.Charles speed was $15$ Kmph and Smith's speed was $12$ kmph.Half an hour later Anthony left the place and and travelled in the same direction.Sometime later he overtakes Smith and $90$ minutes further on he overtakes Charles.What is Anthony's speed?
Thanks for help!
The position of the people is the following. (Assuming Charles and Smith leave at $t=0$, and we use $km$ and $hour$ unit) $$ C(t) = 15t \\ S(t) = 12t \\ A(t) = v(t-0.5) $$ At some point they meet : $$ A(t) = S(t) \implies v(t-0.5) = 12t \\ A(t+1.5) = C(t+1.5) \implies v(t+1) = 15(t+1.5) $$ Solving these equations give $t = 1.5,\ v = 18$.