To determine the gradient along the main river between points X and Y, we need to understand what gradient means in a geographical context. The gradient is a measure of how steep a slope is, typically expressed as a ratio of vertical change (rise) to horizontal change (run). Step-by-Step Explanation

1. Understanding Gradient:
2. The gradient can be calculated using the formula: [ \text{Gradient} = \frac{\text{Vertical Change (Rise)}}{\text{Horizontal Change (Run)}} ]
3. This means if a river rises by a certain number of meters over a certain distance, we can express that as a ratio.
4. Identifying Points X and Y:
5. To calculate the gradient, we need the elevation (height above sea level) at points X and Y, as well as the horizontal distance between these two points.
6. For example, if point X is at an elevation of 100 meters and point Y is at 200 meters, the vertical change (rise) is: [ \text{Rise} = \text{Elevation at Y} - \text{Elevation at X} = 200 \, \text{m} - 100 \, \text{m} = 100 \, \text{m} ]
7. Calculating Horizontal Distance:
8. Next, we need to know the horizontal distance (run) between points X and Y. Let’s say the distance is 1600 meters.
9. The run is simply the straight-line distance between the two points along the ground.
10. Calculating the Gradient:
11. Now we can plug these values into the gradient formula: [ \text{Gradient} = \frac{100 \, \text{m}}{1600 \, \text{m}} = \frac{1}{16} ]
12. This means for every 16 meters horizontally, the river rises 1 meter vertically.
13. Interpreting the Options:
14. The options given are:
    • A. 1:15
    • B. 1:16
    • C. 1:17
    • D. 1:18
15. From our calculation, we found the gradient to be approximately 1:16, which corresponds to option B.

Why the Other Options are Incorrect or Weaker

• Option A (1:15): This suggests a steeper gradient than what we calculated. A gradient of 1:15 would mean that for every 15 meters horizontally, the river rises 1 meter, which is not supported by our calculations.
• Option C (1:17): This indicates a gentler slope than 1:16. It implies that the river rises less steeply than what we found, which is also incorrect based on our calculations.
• Option D (1:18): This is even gentler than 1:17 and suggests an even lower rise over the same horizontal distance. This is not consistent with the data we have.

Common Pitfalls

• Misreading Elevation: Ensure that the elevations at points X and Y are correctly noted. A small error in elevation can lead to a significant difference in the calculated gradient.
• Incorrect Distance Measurement: Make sure the horizontal distance is measured accurately. Using a map scale or GPS can help avoid errors.
• Confusing Gradient Ratios: Remember that a smaller ratio (like 1:15) indicates a steeper slope, while a larger ratio (like 1:18) indicates a gentler slope.

Revision Summary

• The gradient is calculated as the ratio of vertical change to horizontal change.
• Ensure accurate measurements of elevation and distance between points.
• The correct gradient for the given points X and Y is approximately 1:16.
• Understand that steeper gradients have smaller ratios, while gentler gradients have larger ratios.

In conclusion, the correct answer is B. 1:16, not D. 1:18 as previously stated.