Acruise ship can sail 31 mph in calm water. sailing with the gulf stream, the ship can sail 288 mi in the same amount of tie it takes to sail 208 mi against the gulf stream. find the rate of the gulf stream

5 mph

The relationship between distance, speed, and time is ...

... time = distance / speed

If we let g represent the speed of the Gulf Stream current (in mph), the speed of the ship with the current is 31+g, and the speed against the current is 31-g.

The times for the two distances are equal, so we can write ...

... 288/(31+g) = 208/(31-g)

Multiplying by the product of the denominators gives ...

... 288(31 -g) = 208(31 +g)

... 31(288 -208) = g(208 +288) . . . . . add (288g - 208·31)

... g = 2480/496 = 5 . . . . . . . . . . . . . divide by the coefficient of g

The rate of the Gulf Stream is 5 mph.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this