Question

Round 1: Car A and Car B start moving in opposite direction to each other from two different points which are 22.4 Km apart. They meet after 2 hours.

Round 2: Car A and Car B start from same point in same direction and after 3 hours, difference of their covered distance becomes 26.4 Km.

Given that speed of both cars remains same in both rounds and speed of car A > speed of car B.

Find the speed of Car A(in Km/hr).

Answer 1

Let the speed of Car A be $x\text{Km/hour}.$
And the speed of the Car B be $y\text{Km/hour}.$

In two hours, both cars meet.
Hence, sum of distance, covered by both cars individually, become equal to distance between their starting points.
$\Rightarrow 2(x+y)=22.4$
$\Rightarrow x+y=11.2...\left(a\right)$

Given, in the same direction, difference of their covered distance in 3 hour is 26,4 Km.
$\Rightarrow 3(x-y)=26.4...\left(b\right)$

Multiply (a) by $3$ on both side and subtract it from (b) to eliminate $x.$

$3(x-y)-3(x+y)=26.4-3\times 11.2$
$\Rightarrow -3y-3y=-7.2$
$\Rightarrow y=\frac{7.2}{6}=1.2$

$\therefore$ Speed of Car B is $1.2\text{Km/hr}.$
$\therefore$ Speed of Car A is
$11.2-1.2=10\text{Km/hr}.$