Places A and are 45 km apart from each other. A car starts from place A and another car starts from place at the same time. If they move in the same direction, they meet in 4 and a half hour and if they move towards each other, they meet in 27 minutes. What is the speed (in km/h) of the car which moves faster?

55

Let speed of faster car = x km/h

Speed of slower car = y km/h

Relative speed when car moves in same direction = ( x - y ) km/h

Relative speed when car moves in opposite direction = ( x + y ) km/h

According to question ,

\(\frac{45}{x - y }\) = 4.5

( x - y) = 10   --------(1)

Now ,

\(\frac{45}{x + y }\) = \(\frac{27}{60}\) 

\(\frac{45}{x + y }\) = \(\frac{9}{20 }\) 

( x + y) = 100

( x+ y) = 100   -------(2)

Adding equation 1 & equation 2

2x = 110

x = 55

So , the speed of faster car is 55 km/h .