a motorboat travels 22 mph with the current and 8 mph against the current. Find the speed of the boat in still water and the speed of the current.
Vb + Vc = 22
Vb - Vc = 8
Add the Eqs:
2Vb = 30
Vb = 15 mph.
Replace Vb in Eq1 with 15:
15 + Vc = 22
Vc = 7 mph = Velocity of the current.
To find the speed of the boat in still water and the speed of the current, we can set up a system of equations.
Let's represent the speed of the boat in still water as "b" and the speed of the current as "c".
When the boat is traveling with the current, its effective speed is the sum of the boat's speed and the speed of the current. Therefore, we can write the equation:
b + c = 22 (1)
Similarly, when the boat is traveling against the current, its effective speed is the difference between the boat's speed and the speed of the current. We can write the equation:
b - c = 8 (2)
Now, we have a system of two equations with two variables. We can solve it by either substitution or elimination.
Let's use the elimination method to solve this system:
Adding equation (1) and equation (2) together eliminates the "c" term:
(b + c) + (b - c) = 22 + 8
2b = 30
Divide both sides of the equation by 2 to solve for b:
2b/2 = 30/2
b = 15
So, the speed of the boat in still water is 15 mph.
Now, let's substitute the value of b into equation (1) to solve for c:
15 + c = 22
c = 22 - 15
c = 7
Therefore, the speed of the current is 7 mph.
In summary, the speed of the boat in still water is 15 mph, and the speed of the current is 7 mph.
To find the speed of the boat in still water and the speed of the current, you can set up a system of equations using the given information.
Let's assume the speed of the boat in still water is represented by "b" and the speed of the current is represented by "c".
When the motorboat is traveling with the current, its speed is 22 mph. This means that the boat's speed in still water (b) added to the speed of the current (c) equals 22:
b + c = 22 -- Equation 1
When the motorboat is traveling against the current, its speed is 8 mph. This means that the boat's speed in still water (b) minus the speed of the current (c) equals 8:
b - c = 8 -- Equation 2
Now we have two equations (Equation 1 and Equation 2) with two variables (b and c). We can solve this system of equations by using the method of substitution or elimination.
Let's use the method of elimination to solve this system:
1. Multiply Equation 2 by -1 to change the signs:
-b + c = -8 -- Equation 3
2. Add Equation 1 and Equation 3:
(b + c) + (-b + c) = 22 + (-8)
2c = 14
3. Simplify:
2c = 14
c = 7
We have found the value of the current speed, which is 7 mph.
4. Now, substitute the value of c (7) into Equation 1:
b + 7 = 22
5. Solve for b:
b = 22 - 7
b = 15
The speed of the boat in still water is 15 mph and the speed of the current is 7 mph.