SOLUTION: SOLVE USING DETERMINANTS and CRAMER'S RULE A team of rowers can row 4 kilometers downstream in 8 minutes, but it takes 12 minutes for the team to row the same distance upstream

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Question 208210: SOLVE USING DETERMINANTS and CRAMER'S RULE
A team of rowers can row 4 kilometers downstream in 8 minutes, but it takes 12 minutes for the team to row the same distance upstream. How fast can the team row in still water, and what is the rate of the current?
Answer by pjalgeb(9) (Show Source):
You can put this solution on YOUR website!
Given:
4 km. = distance travelled
8 minutes = time it takes to row downstream

12 minutes = time it takes to row upstream

Required:
Find x (Speed in still water) and y (Rate of the current).

Solution:

Rates per hour:
= hours
= hours

Distance = Speed * Time

Speed(Kph) Time(h) Distance(K)
_______________________________________________
Downstream | x+y : 2/15 : (x+y)(2/15) |
Upstream | x-y : 1/5 : (x-y)(1/5) |
_______________________________________________
Since the distances are the same(4km) then we can have the following Equations:

+ = 4) * 15
2x + 2y = 60 --> Equation 1

- = 4) * 5)
x - y = 20 --> Equation 2

Now we have two equations with two unknowns:
2x + 2y = 60 --> Equation 1
x - y = 20 --> Equation 2

The augmented 2x2 matrix for the above system of equations is:
| 2 2 | 60 |
| 1 -1 | 20 |

Using Cramer's Rule:

First we solve for D, Dx and Dy:
D = | 2 2 | = 2(-1) - 2(1) = - 2 - 2 = - 4
| 1 -1 |
since D is not 0 then we can proceed:

Dx = | 60 2 | = 60(-1) -2(20) = -60 - 40 = -100
| 20 -1 |

Dy = | 2 60 | = 2(20) - 60(1) = 40 - 60 = -20
| 1 20 |

Now we can solve for x and y:

ANSWER:
The team can row 25 kph in still water and the current has a rate of 5 kph.