Question

Signs are placed at regular intervals along a mountain road to indicate altitude. At Grinbrir Lodge, the sign indicates an elevation of 876 meters. But 17 kilometers down the road, another sign indicates that the elevation is 672 meters. What is the average elevation change per kilometer traveled from the Lodge

Answer 1

-12 m/km

Explanation:

You want to know the average elevation change per kilometer given the elevation changes from 876 meters to 672 meters over a distance of 17 kilometers.

Rate of change

The average elevation change per kilometer is found by dividing the elevation change by the number of kilometers. The elevation change is the difference between the ending elevation and the starting elevation.

rate of change = ((end elevation) -(start elevation))/(distance)

= (672 m -876 m)/(17 km) = (-204 m)/(17 km) = -12 m/km

The average elevation change is -12 meters per kilometer traveled from the lodge.

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Additional comment

Expressing both dimensions in the same unit, we can find the average grade of the road to be ...

(-12 m)/(1000 m) = -0.012 = -1.2% . . . . . average grade of the road