Peter belongs to Town A and Paul belongs to Town B. They start their journeys towards each other’s towns following the same route at the same time. They meet some where on the way and continue with their journeys. After meeting Paul, Peter takes another 13.5 hours to reach his destination while Paul takes another 6 hours to reach Peter’s town. If Peter travelled at the speed of 30 km/h, what was Paul’s speed in km/h?

Let they meet at point T after time t. Let the speed of B = x kmph

Consider the distance AT. It was covered by paul in 6 hours and peter in t hours.

Hence ,

6x = 30t..........................eq1

Consider the distance BT. It was covered by paul in t hours and peter in 13.5 hours.

Hence,

$$13.5 \times 30 = xt$$ ..................eq2

Dividing eq1 by eq2 we get;

$$\frac{6x}{13.5\times30} = \frac{30t}{xt}$$

$$6{x^2} = {30\times13.5\times30}$$

$${x^2} = 2025$$

 x = 45 km/h

Hence the speed of paul is 45 km/h