There are two cars...

Question

Let's imagine a $6000 km$ stretch of road. Now, there are two cars $A$ and $B$, each with average speeds of $100km/h$ (for $A$) and $250km/h$ (for $B$) respectively. If $A$ is given a headstart of $1000km$ (i.e. once $A$ reaches the $1000km$ mark, $B$ will start moving), at what point on the $6000km$ stretch of road will the two cars meet, assuming they maintain a constant speed?

They are moving in the same direction (Eastward).

P.S. I tried calculating it tediously by acknowledging the distance between them after each hour. They should meet in about six hours if I'm correct, but i can't pin down the exact value.

Answer 1

Solve $$\frac{d-1000}{100} = \frac{d}{250}.$$

Answer 2

First calculate $t$ (meeting time) from following equation :

$1000+v_A \cdot t =v_B \cdot t$

where $v_A$ and $v_B$ are speeds of cars $A$ and $B$ ,

then , find meeting point $l$ from :

$l=v_B \cdot t$

Answer 3

Assuming they move in same direction.

Their relative separation when B starts moving is $1000$ km.

Their relative velocity $=250-100 =150$ km.

Using, $s_r=s_{\circ}+ut+\frac{1}{2}at^2$

$0=1000+150t+\frac{1}{2}\cdot0\cdot t^2$

$t=\dfrac{1000}{150}=6.6667$

Total distance $=s_{\circ}+u\cdot t$

$=1000+100\cdot6.6667=1666.67$