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

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.