Question

Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?

How do I put this into two equation and use the matrix to solve it?

Answer 1

u = 2d
or
u - 2d = 0
u + d = 5

so the matrix would be

1 -2 0
1 1 5

add -1 times the 1st row to the 2nd row. Then you get

1 -2 0
0 3 5

multiply the 2nd row by 1/3:

1 -2 0
0 1 5/3

The 2nd row tells us that d = 5/3, so u = 10/3

Answer 2

I don't know about the matrix, but it is not necessary to solve the problem.

x = time traveling down river
2x = time traveling up river.

x + 2x = 5

3x = 5

x = 5/3 hour = 1 hour, 40 minutes

2x = ?

I hope this helps.