a rowing team rowed an average of 17.2 miles per hour with he current and 10.4 miles per hour against the current. Determine the teams rowing speed in still water and speed of the current
row: (17.2+10.4)/2 = 13.8
water: 13.8-10.4 = 3.4
To determine the team's rowing speed in still water and the speed of the current, we can use the concept of relative velocity.
Let's assume the rowing speed in still water is represented by "x" (in miles per hour), and the speed of the current is represented by "c" (in miles per hour).
When rowing with the current, the team's effective speed is the rowing speed in still water plus the speed of the current: x + c.
When rowing against the current, the team's effective speed is the rowing speed in still water minus the speed of the current: x - c.
Given that the team rowed an average of 17.2 miles per hour with the current, we can set up the equation:
(x + c) + (x - c) = 17.2
Simplifying the equation, we get:
2x = 17.2
Dividing both sides by 2, the equation becomes:
x = 8.6
So, the team's rowing speed in still water is 8.6 miles per hour.
Now, we can substitute this value into one of the equations to find the speed of the current.
Using the equation (x + c) = 17.2, and substituting x = 8.6, we get:
8.6 + c = 17.2
Subtracting 8.6 from both sides, we have:
c = 17.2 - 8.6
Therefore, the speed of the current is 8.6 miles per hour.
To summarize:
- The team's rowing speed in still water is 8.6 miles per hour.
- The speed of the current is 8.6 miles per hour.
To determine the rowing speed in still water and the speed of the current, we can use the formula:
Rowing speed in still water (r) + Speed of the current (c) = Rowing speed with the current
Rowing speed in still water (r) - Speed of the current (c) = Rowing speed against the current
Let's assign variables to the unknowns:
Rowing speed in still water = r
Speed of the current = c
Given:
Average speed with the current = 17.2 mph
Average speed against the current = 10.4 mph
Using the two equations above, we can set up a system of equations:
r + c = 17.2 ----(1)
r - c = 10.4 ----(2)
To solve this system of equations, we can use the method of elimination. Adding equations (1) and (2) eliminates the variable "c":
(r + c) + (r - c) = 17.2 + 10.4
2r = 27.6
Dividing both sides by 2:
r = 13.8 mph
Now we can substitute the value of r in one of the original equations to find the value of c. Let's use equation (1):
13.8 + c = 17.2
c = 17.2 - 13.8
c = 3.4 mph
Therefore, the team's rowing speed in still water is 13.8 miles per hour, and the speed of the current is 3.4 miles per hour.