On a topographical map with a scale of 1 : 60,000, a railway track connects Hill Station X… — JAMB UTME

On a topographical map with a scale of $1 : 60,000$ , a railway track connects Hill Station $X$ at an elevation of $460\text{ m}$ to Junction $Y$ at an elevation of $340\text{ m}$ . If the distance between the two points measured along the map is $5\text{ cm}$ , what is the average gradient of the slope between Station $X$ and Junction $Y$ ?

A
$1 \text{ in } 50$
$1 \text{ in } 25$ Answer
C
$1 \text{ in } 5$
D
$1 \text{ in } 2,500$

Answer

The average gradient between Station X and Junction Y is

1 \text{ in } 25

The vertical interval between the two stations is

460\text{ m} - 340\text{ m} = 120\text{ m}

. Using the map scale of

1 : 60,000

, a map distance of

5\text{ cm}

represents a ground horizontal distance of

5 \times 60,000\text{ cm} = 300,000\text{ cm} = 3,000\text{ m}

. Dividing the vertical interval by the horizontal equivalent gives

\frac{120}{3000} = \frac{1}{25}

, which is expressed as

1 \text{ in } 25

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 460\text{ m} - 340\text{ m} = 120\text{ m}

The Vertical Interval is the absolute difference in elevation between the two points.

Calculate the Horizontal Equivalent (HE) in meters

\text{HE} = 5\text{ cm} \times 60,000 = 300,000\text{ cm} = 3,000\text{ m}

Convert the measured map distance to ground distance using the representative fraction scale, then convert centimeters to meters.

Calculate the gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{120\text{ m}}{3,000\text{ m}} = \frac{1}{25} \text{ or } 1 \text{ in } 25

Express the ratio of Vertical Interval to Horizontal Equivalent in standard

1 \text{ in } N

form by dividing both values by the vertical interval.

Key Concept

Topographic Gradient Calculation

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