Question

Point $A$ and $B$ are $70km$ apart on a highway. A car starts from $A$ and another car starts from $B$ at the same time. If they travel in the same direction, they meet in $7$ hours, but if they travel towards each other they meet in one hour. What are their speeds?

• A. $30km/hr$ and $40km/hr$
• B. $36km/hr$ and $40km/hr$
• C. $19km/hr$ and $20km/hr$
• D. $40km/hr$ and $50km/hr$

Answer 1

Answer: (A)

$30km/hr$ and $40km/hr$

Let car speed from point $A=xkm/hr$.
and car speed from point $B=ykm/hr$.

Distance = speed $\times$ time
$\therefore$ Distance from $A=x\times 7=7x$
Distance from $B=y\times 7=7y$
If they travel in the same direction, they meet in $7$ hours. Point $A$ and $B$ are $70km$ apart.
$\Rightarrow 7x-7y=70$
$\Rightarrow x-y=10$ ...$\left(i\right)$

if they travel towards each other they meet in one hour. Point $A$ and $B$ are $70km$ apart.
$x+y=70$ ...$\left(ii\right)$

Adding $\left(i\right)$ and $\left(ii\right)$. we get
$2x=80$
$\therefore x=40$

substituting $x=40$ in $\left(i\right)$. we get
$40-y=10$
$\therefore y=30$
$\therefore x=40km/hr$ and $y=30km/hr$.