A bicyclist was going from point A to point B with a speed of 12 km/h. On the way back he increased his speed to 18 km/h and covered the distance in 15 minutes less. What is the distance between point A and point B?

velocity=distance / time   ⇒ distance=velocity x time.

x=time spent to go from point A to point B.
(x-15)=time spent to go from point A to point B.

Distance from point A to B=distance from point B to A

12x=distance from point A to B
18(x-15)= distance form point B to A
we have the following equation:
12x=18(x-15)
12x=18x-270
18x-12x=270
6x=270
x=270/6
x=45

45 minutes=45 minutes(1 hour/ 60 minutes)=0.75 hours

distance between point A and point B=12x=12km/h(0.75 h)=9 km

Answer: the distance between point A and point B would be 9 km.