A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 4 km per day and it will take them two days, how many kilometres long is the route down the mountain?

Let the speed of the group when going up be A and therefore, the speed of the group when going down = $$\dfrac{3A}{2}$$

=> Time taken by both routes is the same, and it is given that they go up in 2 days.

=> Speed of group when going up = A = 4km/day

Therefore, speed of the group when going down = $$\dfrac{3A}{2}$$ = 6km/day

Since, the time taken is the same, time taken going down = 2 days

Hence, the length of route down the mountain = 6*2 = 12 km 

The answer is option A.