Question

The distance between two places A and B on a road in 7O Km. 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 hrs, but if they travel towards each other they meet in 1hr. What are their speeds ?​

Answer 1

$\huge{ \fbox{ \fbox \mathtt \blue{Question:-}}}$

⇒ The distance between two places A and B on a road in 7O Km. 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 hrs, but if they travel towards each other they meet in 1hr. What are their speeds ?​

$\huge{ \fbox{ \fbox \mathtt \blue{Solution:-}}}$

⇒ When they travel in same direction, suppose  they meet when B travels for x m, then A will have travelled (70+x )m in the same time.

⇒ As , we know that

→ $\sf Speed = \frac{Distance}{Time}$

→  $\sf Speed\:for\:Car\:at\:A\:= \: \frac{x+70}{7}$

→ $\sf And\:Speed\:of\:Car\:at\:B\:=\: \frac{x}{7}$

⇒ And when they travel in the opposite direction, suppose they meet when A  travels for ( y )m, then B will have travelled (70−y) m in the same  time

→ $\sf Speed\:of\:Car\:at\: A\:=\: \frac{y}{1} \:=\: 1$

→ $\sf And\:Speed\:of\:Car\:at\:B\:=\: \frac{70-y}{1} \:=\: 70-y$

${\huge{\rm{\underline{\underline{Equating\:the\:speeds\:of\:the\:cars\:in\:both\:the\:cases :-}}}}}$

→ $\sf Speed\:of\:Car\:at\:A\:=\: \frac{x+70}{7} = y$

→ $\sf x + 70 = 7y$

$\sf => x - 7y = -70 -- (i)$

→ $\sf Speed\:of\:Car\:at\:B\:=\: \frac{x}{7} = 70 - y$

$\sf => x + 7y = 490 -- (ii)$

${\huge{\rm{\underline{\underline{Adding\:Equation\:(i)\;and\:(ii)\: :-}}}}}$

→ $\sf 2x = 420$

$\sf => x = 210$

______

⇒ So ,

→ $\sf Speed\:of\:Car\:at\:A\:=\: \frac{x+70}{7}$

→  $\sf \frac{280}{7} = \: 40\:km/hr$

→ $\sf Speed\:of\:Car\:at\:B\:=\: \frac{x}{7}$

→ $\sf \frac{210}{7} = \: 30\:km/hr$