To answer this problem, we will use the formula of hypotenuse:
c^2 = a^2 + b^2
Where,
c = total distance traveled / displacement = 119 miles
a = distance traveled north = 5 hours * x mph = 5 x
b = distance traveled west = 4 hours * (x + 5) mph = 4 (x + 5)
Substituting to the equation:
119^2 = (5 x)^2 + [4(x + 5)]^2
14,161 = 25 x^2 + 16 (x + 5)^2
14,161 = 25 x^2 + 16 (x^2 + 10 x + 25)
14,161 = 25 x^2 + 16 x^2 + 160 x + 400
0 = 41 x^2 + 160 x – 13,761
x =[ - b ± sqrt (b^2 – 4ac)]/ 2a
x = [- 160 ± sqrt (160^2 – 4 * 41 * (– 13,761))] / 2 * 41
x = - 1.95 ± 18.42
x = -20.37 , 16.47
Since speed cannot be negative, therefore x = 16.47
Therefore the speed of the ship travelling west is:
x + 5 = 21.47 mph (ANSWER)
