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Places A and B are $160$ km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in $4$ hours. If they travel towards each other, they meet in $1$ hour $36$ minutes. What are the speeds of the two cars ?
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Sol. Let the speed of two cars be $x$ km/h $\& y$ km/h respectively ($x > y$).
Therefore $4x - 4y = 160$ or $x - y = 40$ ----- (i)
$1$ hour $36$ minutes = $1.6$ hours
$\therefore 1.6x + 1.6y = 160$ or $x + y = 100$ ----- (ii)
Solving (i) and (ii), we have
$x = 70$ and $y = 30$
$\therefore$ speed of two cars are $70$ km/h and $30$ km/h respectively.
Therefore $4x - 4y = 160$ or $x - y = 40$ ----- (i)
$1$ hour $36$ minutes = $1.6$ hours
$\therefore 1.6x + 1.6y = 160$ or $x + y = 100$ ----- (ii)
Solving (i) and (ii), we have
$x = 70$ and $y = 30$
$\therefore$ speed of two cars are $70$ km/h and $30$ km/h respectively.