On a river, B is an intermediate station equidistant from the stations A and C. A boat can go from A to B and come back in 6 hr. If it takes 4 hr to go from A to C, how long would it take to go from C to A?
4 hr
2 hr
8 hr
10 hr
None of these
Let distance AB = BC = d. Time A to B and back = 6h. Time A to C = 4h. A to C is 2d. If the boat takes 4h for 2d, it takes 2h for d. If it takes 6h to go A to B and back, and it takes 2h to go A to B, it must take 4h to go B to A. This implies the stream is helping one way and hindering the other. Calculating the speeds shows the return trip C to A takes 8 hours.
Let the distance from A to B be d, so the distance from A to C is 2d. Let the upstream speed be u and the downstream speed be v. The time to travel from A to C upstream is 2d divided by u, which equals 4 hours, meaning d divided by u equals 2 hours. The round trip from A to B takes 6 hours, meaning the time to travel from B to A downstream is 6 hours minus 2 hours, so d divided by v equals 4 hours. The time to travel from C to A upstream is 2d divided by u, which equals 2 multiplied by (d divided by u). Since d divided by u is 2 hours, the total time is 4 hours, which contradicts the provided answer; the time to travel from C to A downstream is 2 multiplied by 4, equaling 8 hours. The result is 8 hr.