On Map A, a straight section of a railway track connecting two transport terminals measure… — JAMB UTME

On Map A, a straight section of a railway track connecting two transport terminals measures $18.0\text{ cm}$ . Map A is drawn to a statement scale of $2\text{ cm}$ to $1\text{ km}$ . If this identical section of railway is represented on Map B, which is drawn to a Representative Fraction (R.F.) scale of $1 : 150,000$ , what will be the length of the railway track on Map B?

A
$24.0\text{ cm}$
$6.0\text{ cm}$ Cevap
C
$12.0\text{ cm}$
D
$54.0\text{ cm}$

Cevap

The length of the railway track on Map B is

6.0\text{ cm}

The correct answer is

6.0\text{ cm}

. The statement scale of

2\text{ cm}

1\text{ km}

means that

1\text{ cm}

on Map A represents

0.5\text{ km}

on the ground. A measured length of

18.0\text{ cm}

therefore corresponds to an actual ground distance of

9.0\text{ km}

(

900,000\text{ cm}

). When represented on Map B with an R.F. scale of

1 : 150,000

, the new map distance is calculated by dividing

900,000\text{ cm}

150,000

, giving exactly

6.0\text{ cm}

Adım Adım Çözüm

Determine the actual ground distance using the statement scale of Map A.

Map A scale is

2\text{ cm} = 1\text{ km}

, so

1\text{ cm} = 0.5\text{ km}

. Ground distance

= 18.0\text{ cm} \times 0.5\text{ km/cm} = 9.0\text{ km}

Before calculating distance on a second map, the actual real-world ground distance must be determined.

Convert the ground distance from kilometers to centimeters.

9.0\text{ km} = 9.0 \times 100,000\text{ cm} = 900,000\text{ cm}

Map measurements in Representative Fraction (R.F.) calculations require consistent units of measurement.

Calculate the map length on Map B using its R.F. scale (

1 : 150,000

Map length on Map B

= \frac{\text{Ground Distance}}{\text{Scale Denominator}} = \frac{900,000\text{ cm}}{150,000} = 6.0\text{ cm}

Dividing the ground distance in centimeters by the R.F. denominator gives the corresponding distance on the new map.

Anahtar Kavram

Multi-step conversion between statement scales, ground distances, and representative fraction (R.F.) map scales

Tahmini Süre:2m 0s

Soru

Cevap

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