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The speed of Boat P is 3 km/h more than the speed of Boat Q. The time taken by Boat Q to travel a distance of 30 km downstream is 30 minutes more than the time taken by Boat P to travel the same distance downstream. If the speed of the current is 1/3 of the speed of Boat Q, then what is the speed of Boat P?

The speed of Boat P is 3 km/h more than the speed of Boat Q. The time taken by Boat Q to travel a distance of 30 km downstream is 30 minutes more than the time taken by Boat P to travel the same distance downstream. If the speed of the current is 1/3 of the speed of Boat Q, then what is the speed of Boat P? Correct Answer 12

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

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