A and B are two diametrically opposite points on a circular road whose

Solution:

The distance between A and B around the road is 3 km since the entire circumference of the circular road is 6 km.

We can let r = the speed of the cyclist in completing the first circle. Notice that the distance traveled between the first time he passes through point B and the second time he passes it is the circumference of the road, or 6 km. However, the first 3 km of this 6 km is the 2nd half of the first circle in which his speed is r km/hr and the last 3 km is the 1st half of the second circle, in which his speed is (r - 3) km/hr. Therefore, we can create the equation:

3/r + 3/(r - 3) = 5/6

Multiplying the equation by 6r(r - 3), we have:

18(r - 3) + 18r = 5r(r - 3)

18r - 54 + 18r = 5r^2 - 15r

5r^2 - 51r + 54 = 0

(5r - 6)(r - 9) = 0

r = 6/5 or r = 9

Although both values of r are positive, r can’t be 6/5, otherwise, r - 3 would be negative. Therefore, r = 9.

Answer: D