On a topographic map drawn to a Representative Fraction (RF) scale of 1 : 60,000, a linear… — JAMB UTME

On a topographic map drawn to a Representative Fraction (RF) scale of $1 : 60,000$ , a linear segment of a river between two hydrological gauging stations measures $22.5\text{ cm}$ . What is the actual ground distance between the two stations in kilometers?

Answer: 13.5 km

Answer

The actual ground distance between the two stations is

13.5\text{ km}

The ground distance is obtained by scaling up the map distance using the Representative Fraction:

22.5\text{ cm} \times 60,000 = 1,350,000\text{ cm}

. Converting to kilometers (

1\text{ km} = 100,000\text{ cm}

) yields

13.5\text{ km}

Step-by-Step Solution

Calculate the ground distance in centimeters using the Representative Fraction

Ground distance in cm =

22.5\text{ cm} \times 60,000 = 1,350,000\text{ cm}

The RF scale of

1 : 60,000

indicates that

1\text{ cm}

on the map represents

60,000\text{ cm}

on the ground.

Convert the ground distance from centimeters to kilometers

Ground distance in km =

\frac{1,350,000\text{ cm}}{100,000\text{ cm/km}} = 13.5\text{ km}

There are

100,000\text{ cm}

1\text{ km}

(

100\text{ cm/m} \times 1,000\text{ m/km}

Key Concept

Map Scale Conversion and Ground Distance Calculation

Estimated Time:1m 30s

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