A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?

 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

let w = time heading west at 25 mph

the total time is 7 hrs, therefore

(7-w) = time heading north at 19 mph

Distance = speed * time

25w + 19(7-w) = 145

25w + 133 - 19w = 145

25w - 19w = 145 - 133

6w = 12

w = 12/6

w = 2 hrs traveling west

therefore

2 * 25 = mile going west

Confirm this solution, 7 - 2 = 5 hrs going north

19 * 5 = 95mi

25 * 2 = 50mi

total dist 145 mi

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column