Question

A boat sails downstream from a point P to point Q, which is 24 km away from P, and then returns to P. If the actual speed of the boat (in still water) is 6 km/h, the entire trip from P to Q takes 3 hours less than that from Q to P. What should be the actual speed (in km/h) of the boat to sail from P to Q in 2 hours?

Options

• 22

• 12

• 15

• 10

Answer 1

10

Explanation:

Let the speed of Current (CS) be x

Boat speed (BS) = 6 km/hr

Distance = 24 km

A.T.P.

⇒ `24/(6 + x) = 24/(6 - x) - 3`

⇒ `24/(6 + x) = (24 - 18 + 3x)/(6 - x)`

⇒ `144 - 24x = 144 + 24x - 108 - 18x + 18x + 3x^2`

⇒ `3x^2 + 24x + 24x - 108` = 0

⇒ `x^2 + 16x - 36` = 0

⇒ `x^2 + 18x - 2x - 36` = 0

⇒ `x(x + 18) - 2(x + 18) = 0`

⇒ `(x - 2)(x + 18)` = 0

∴ `x` = 2

∴ Current speed = 2 km/hr

∴ A.T.P.

`24/(B_s + 2)` = 2

⇒ 2B_s + 4 = 24

⇒ 2B₅ = 20

⇒ B₅ = 10

∴ Boat speed will be 10 km/hr.