GIVEN : The speed of Boat P is 3 km/h more than the speed of Boat Q. Speed of the current is 1/3 of the speed of Boat Q CALCULATION : Speed of boat Q = x km/h Speed of P = (x + 3) km/h And, Speed of current = (x/3) km/h ∴ Speed of boat P downstream = x + 3 + x/3 = (4x + 9)/3 ∴ Speed of boat Q downstream = x + x/3 = 4x/3 The time taken by Boat Q to travel 30 km downstream is 30 minutes more than the time taken by Boat P ∵ Distance covered = Speed × Time taken 30/ + 30/60 = 30/(4x/3) + ½ = 90/4x ⇒ 378x + 8x2 = 90(4x + 9) ⇒ 378x + 8x2 = 360x + 810 ⇒ 8x2 + 18x - 810 = 0 ⇒ 8x2 + 90x - 72x - 810 = 0 ⇒ x(8x + 90) - 9(8x + 90) = 0 ⇒ (8x + 90)(x - 9) = 0 ⇒ x = 9 (∵ x can’t be negative) ∴ Speed of P = (9 + 3) km/h = 12 km/h