SOLUTION: A boat took 5 hours to travel 60 kilometers up a river against a current. The return trip took 3 hours .Find the speed of the boat in still water and the speed of the current.
Question 200406: A boat took 5 hours to travel 60 kilometers up a river against a current. The return trip took 3 hours .Find the speed of the boat in still water and the speed of the current.
Solve the linear system
x-2/3 + y+1/5 = 2
x+2/7 - y+5/3 = -2
You can put this solution on YOUR website! A boat took 5 hours to travel 60 kilometers up a river against a current.
The return trip took 3 hours
.Find the speed of the boat in still water and the speed of the current.
:
Let x = speed of the boat in still water
Let y = speed of the current
then
(x+y) = speed downstream
(x-y) = speed upstream
:
Write a dist equation for each trip: Dist = time * speed
:
5(x - y) = 60
3(x + y) = 60
:
Simplify, divide the 1st equation by 5, and the 2nd equation by 3, results:
x - y = 12
x + y = 20
--------------addition eliminates y, find x
2x = 32
x = 16 km/hr boat speed in still water
and
16 + y = 20
y = 20 - 16
y = 4 km/hr current speed
:
Check solution in original 1st equation
5(16 - 4) = 60
:
:
Solve the linear system
Assume it's + = 2 - = -2
:
Get rid of the denominators,
multiply the 1st eq by 15, results:
5(x-2) + 3(y+1) = 15(2)
5x - 10 + 3y + 3 = 30
5x + 3y - 7 = 30
5x + 3y = 30 + 7
5x + 3y = 37
:
Multiply the 2nd equation by 21, results:
3(x+2) - 7(y+5) = 21(-2)
3x + 6 - 7y - 35 = -42
3x - 7y - 29 = - 42
3x - 7y = -42 + 29
3x - 7y = -13
:
Multiply the 1st equation by 3:
15x + 9y = 3(37)
15x + 9y = 111
:
Multiply the 2nd equation by 5
15x - 35y = 5(-13)
15x - 35y = -65
:
Use elimination
15x + 9y = 111
15x - 35y = -65
------------------subtraction eliminate x
+44y = 176
y =
y = 4
:
Use the equation: 5x + 3y = 37 to find x
5x + 3(4) = 37
5x + 12 = 37
5x = 37 - 12
5x = 25
x =
x = 5
:
x = 5, y = 4 is the solution
;
:
Check solution in the 1st original equation + = 2 + = 2 + = 2
