To find the gradient along the river between the two points, we need to understand what gradient means in this context. The gradient is a measure of how steep a slope is, and it is calculated as the vertical change (rise) divided by the horizontal change (run).
Step-by-Step Explanation
- Identify the Vertical Change (Rise):
-
The vertical change between the two points is given as 400 meters. This is the height difference between the two points.
-
Identify the Horizontal Change (Run):
-
The horizontal distance between the two points is given as 10.4 kilometers. To work with consistent units, we need to convert this distance into meters:
[
10.4 \text{ km} = 10.4 \times 1000 \text{ m} = 10400 \text{ m}
]
-
Calculate the Gradient:
- The formula for gradient is:
[
\text{Gradient} = \frac{\text{Vertical Change (Rise)}}{\text{Horizontal Change (Run)}}
]
- Plugging in the values we have:
[
\text{Gradient} = \frac{400 \text{ m}}{10400 \text{ m}} = \frac{400}{10400}
]
- Simplifying this fraction:
[
\frac{400}{10400} = \frac{1}{26}
]
-
This means the gradient is 1 in 26.
-
Interpreting the Result:
- A gradient of 1 in 26 means that for every 26 meters you move horizontally, there is a rise of 1 meter vertically.
Evaluating the Options
Now, let's look at the options provided:
-
A. 1 in 20: This would imply a steeper slope than what we calculated. For every 20 meters horizontally, there would be a 1-meter rise, which is not the case here.
-
B. 1 in 24: This is also steeper than our calculated gradient. It suggests a rise of 1 meter for every 24 meters horizontally, which again does not match our calculation.
-
C. 1 in 26: This is the correct option based on our calculation. It accurately reflects the relationship between the vertical and horizontal distances.
-
D. 1 in 32: This would imply a gentler slope than what we calculated. It suggests a rise of 1 meter for every 32 meters horizontally, which is not consistent with the data provided.
Conclusion
The correct answer is
C. 1 in 26.
Revision Summary
- The gradient is calculated as the vertical change divided by the horizontal change.
- Convert all measurements to the same unit for consistency (meters in this case).
- The calculated gradient of 1 in 26 indicates a rise of 1 meter for every 26 meters of horizontal distance.
- Always evaluate the options against your calculated result to identify the correct answer.