Answer: 19.5 miles or 108.75 miles
Step-by-step explanation:
Let ship traveled to the west x hours and then to the north y hours. Total 7 hours. So we can write 1st equation
x+y=7 (1)
The ship traveled to the west x hours with speed 25 miles/h - the distance 25*x
The ship traveled to the north y hours with speed 19 miles/hour - the distance 19*y
Note that the angle between north and west directions is 90 degrees.
So if the initial traveling point is A, the final travelling point ic C and the point , where ther the ship has changed the travelling direction from West to North is B.
So we have the right triangle ABC, where B angle is right=90 degrees.
AB side=25*x, BC side= 19*y and AC side 145 miles.
According to Pithagor theorem we can write
AC^2=AB^2+BC^2
21025=625*x^2+ 361*y^2 (2)
Solve the system of equations (1) and (2)
y=7-x
625*x^2+361*(7-x)^2=21025
625*x^2+361*(49-14x+x^2)=21025
625*x^2+17689-5054*x+361*x^2=21025
986*x^2- 5054*x-3336=0 dividing on 2 we'll get
493*x^2-2527*x-1668=0
D=3096433 sqrt(D)=appr 1760
x1=(2527-1760)/493/2= appr 0.78 h
x2=(2527+1760)/493/2=appr 4.35 h
So the problem has 2 solutions :
heading west the ship traveled or 0.78*25= 19.5 miles
Or 4.35*25= 108.75 miles
