If a river originates 200 meters above sea level and travels 400 kilometers to the ocean, what is the average gradient in meters per kilometer?

0.2 m/km

5 m/km

0.5 m/km

2 m/km

1 answer

To calculate the average gradient of the river, you can use the formula:

\[ \text{Gradient} = \frac{\text{Change in elevation}}{\text{Distance}} \]

In this case, the change in elevation is from 200 meters above sea level to 0 meters at sea level, which is a change of 200 meters. The distance the river travels is 400 kilometers.

First, we need to convert the distance from kilometers to meters:

\[ 400 \text{ km} = 400,000 \text{ meters} \]

Now, substituting the values into the formula:

\[ \text{Gradient} = \frac{200 \text{ meters}}{400,000 \text{ meters}} \]

Calculating this gives:

\[ \text{Gradient} = 0.0005 \text{ meters per meter} \]

To convert this to meters per kilometer, we multiply by 1000:

\[ \text{Gradient} = 0.0005 \text{ m/m} \times 1000 = 0.5 \text{ m/km} \]

Thus, the average gradient of the river is:

\[ \boxed{0.5 \text{ m/km}} \]