A map scale and a cross-section use different denominators

A fictional surveying worksheet uses a horizontal map scale of 1:50,000. Two points are separated by 6 centimeters on the map, and their elevations are 400 meters and 700 meters. The exercise says to treat that measured separation as horizontal ground distance; it does not ask for a winding walking route. A separate profile uses the same horizontal scale but a vertical scale of 1:5,000. One student converts the map separation to 300 meters, another to 3 kilometers. A third writes that the gradient is 100 percent because the elevation difference is 300 meters. The worksheet also asks whether the profile appears steeper than the real ground. No local surveying standard, property boundary or engineering design is involved. All lengths and simplifying assumptions needed for the calculation are provided, so the answer should show unit conversion before introducing any percentage or exaggeration factor.