Answer :
To solve this problem, we need to find the rate at which Geri rows in still water (g) and the rate of the current (c). We use the information given about her rowing distances and times to set up a system of equations.
### Information Given:
1. Downstream: Geri can row 60 km in 4 hours.
2. Upstream: Geri can row 36 km in 4 hours.
### Understanding Downstream and Upstream:
- Downstream: The speed is increased by the current. So, her effective speed is the sum of her rowing speed and the current's speed. This gives us the equation:
[tex]\[
\text{(Rowing Speed + Current Speed) × Time} = \text{Distance}
\][/tex]
[tex]\[
(g + c) \times 4 = 60
\][/tex]
- Upstream: The speed is reduced by the current. So, her effective speed is the difference between her rowing speed and the current's speed. This gives us the equation:
[tex]\[
\text{(Rowing Speed - Current Speed) × Time} = \text{Distance}
\][/tex]
[tex]\[
(g - c) \times 4 = 36
\][/tex]
### Setting Up the Equations:
From the above, we can set the two equations:
1. [tex]\( 4(g + c) = 60 \)[/tex]
2. [tex]\( 4(g - c) = 36 \)[/tex]
### Simplifying the Equations:
Divide both equations by 4 to simplify:
1. [tex]\( g + c = 15 \)[/tex]
2. [tex]\( g - c = 9 \)[/tex]
### Solving the System of Equations:
Now, we solve these two equations simultaneously.
- Add both equations to eliminate [tex]\( c \)[/tex]:
[tex]\[
(g + c) + (g - c) = 15 + 9
\][/tex]
[tex]\[
2g = 24
\][/tex]
[tex]\[
g = 12
\][/tex]
- Substitute [tex]\( g = 12 \)[/tex] back into one of the equations to find [tex]\( c \)[/tex]:
[tex]\[
g + c = 15
\][/tex]
[tex]\[
12 + c = 15
\][/tex]
[tex]\[
c = 3
\][/tex]
### Conclusion:
- The rate Geri rows in still water ([tex]\( g \)[/tex]) is 12 km/h.
- The rate of the current ([tex]\( c \)[/tex]) is 3 km/h.
### Information Given:
1. Downstream: Geri can row 60 km in 4 hours.
2. Upstream: Geri can row 36 km in 4 hours.
### Understanding Downstream and Upstream:
- Downstream: The speed is increased by the current. So, her effective speed is the sum of her rowing speed and the current's speed. This gives us the equation:
[tex]\[
\text{(Rowing Speed + Current Speed) × Time} = \text{Distance}
\][/tex]
[tex]\[
(g + c) \times 4 = 60
\][/tex]
- Upstream: The speed is reduced by the current. So, her effective speed is the difference between her rowing speed and the current's speed. This gives us the equation:
[tex]\[
\text{(Rowing Speed - Current Speed) × Time} = \text{Distance}
\][/tex]
[tex]\[
(g - c) \times 4 = 36
\][/tex]
### Setting Up the Equations:
From the above, we can set the two equations:
1. [tex]\( 4(g + c) = 60 \)[/tex]
2. [tex]\( 4(g - c) = 36 \)[/tex]
### Simplifying the Equations:
Divide both equations by 4 to simplify:
1. [tex]\( g + c = 15 \)[/tex]
2. [tex]\( g - c = 9 \)[/tex]
### Solving the System of Equations:
Now, we solve these two equations simultaneously.
- Add both equations to eliminate [tex]\( c \)[/tex]:
[tex]\[
(g + c) + (g - c) = 15 + 9
\][/tex]
[tex]\[
2g = 24
\][/tex]
[tex]\[
g = 12
\][/tex]
- Substitute [tex]\( g = 12 \)[/tex] back into one of the equations to find [tex]\( c \)[/tex]:
[tex]\[
g + c = 15
\][/tex]
[tex]\[
12 + c = 15
\][/tex]
[tex]\[
c = 3
\][/tex]
### Conclusion:
- The rate Geri rows in still water ([tex]\( g \)[/tex]) is 12 km/h.
- The rate of the current ([tex]\( c \)[/tex]) is 3 km/h.
