Answer :48 km.
Step-by-step explanation:
Let the speed of Belinda be x km/h. Then, the speed of Alice is (x + 2) km/h.
When they meet in 3 hours, the distance between the towns is given by:
Distance = speed * time Distance = (x + 2) * 3 + x * 3 Distance = 6x + 6
When they meet in 4 hours, with Belinda's speed reduced by 1 km/h and Alice's speed two-thirds of her previous speed, the distance between the towns is given by:
Distance = speed * time Distance = (x - 1) * 4 + (2/3)(x + 2) * 4 Distance = 4x - 4 + (8/3)x + (16/3) Distance = (20/3)x + (4/3)
Since the distance between the two towns is the same in both cases, we can set the two expressions for distance equal to each other:
6x + 6 = (20/3)x + (4/3)
Multiplying both sides by 3, we get:
18x + 18 = 20x + 4
Solving for x, we get:
x = 7
Therefore, the speed of Belinda is 7 km/h, and the speed of Alice is 9 km/h.
To find the distance between the two towns, we can use either of the expressions for distance we obtained earlier:
Distance = 6x + 6 = 6(7) + 6 = 48
Therefore, the distance between the two towns is 48 km.