The distance between two piers is S miles. Two boats start moving simultaneously from different piers at speeds R and B respectively. Find the distance D between the boats T hours after they have started moving.

a) in the direction of the first boat, if the first boat moves slower than the second boat,

b) in the direction of the first boat, if the first boat moves faster than the second boat

a. Let the position of the first boat be taken as the zero point or origin. Since the first boat moves with a speed of R in time, T, it covers a distance D' = RT to get to the position D'.

The second boat which is ahead at position S, the distance between the piers, moves with a speed of B in time, T, its position after it it covers a distance BT is D" = S + BT.

Since the first boat moves slower than the second boat and the both move in the direction of the first boat, their distance apart D = D" - D' = S + BT - RT = S + (B - R)T

b. Let the position of the first boat be taken as the zero point or origin. Since the first boat moves with a speed of R in time, T, it covers a distance D' = RT to get to the position D'.

The second boat which is ahead at position S, the distance between the piers, moves with a speed of B in time, T, its position after it it covers a distance BT is D" = S + BT.

Since the first boat moves faster than the second boat and the both move in the direction of the first boat, their distance apart D = D' - D" = RT - S + BT = (R - B)T - S.