Write and solve a system of equations to determine the speed of the boat and the speed of the current.
Traveling downstream a certain boat went 20km/h. Traveling upstream the same boat only went 8 km/h. Find the speed of the current and the speed of the boat if there were no current.
Let x be the speed of the boat in still water, and y be the speed of the current. Then, we can write the following system of equations:
1) x + y = 20 (downstream speed)
2) x - y = 8 (upstream speed)
We can solve this system of equations by adding both equations:
1 + 2) (x + y) + (x - y) = 20 + 8
2x = 28
x = 14
Now that we have the value of x, we can find the value of y by substituting it in either equation. We will use equation 1:
14 + y = 20
y = 6
So, the speed of the boat in still water is 14 km/h, and the speed of the current is 6 km/h.