Question

There are two different maps of California. The scale on the first map is 1 cm to 20 km. The distance from Fresno to San Francisco is 15 cm. The scale on the second map is 1 cm to 100 km. What is the distance from Fresno to San Francisco on the second map? Explain your reasoning.

Answer 1

Given:

• There are two different maps for California.
• Scale of the first map is $1cm to 20km$.
• Distance between Fresno and San Francisco = $15cm$
• Scale of the second map is $1cm to 100km$

To find:

The distance between from Fresno to San Francisco according to the second map.

Note:

Any scale of '$x$' cm to '$y$' km can be expressed in the ratio form which is given by "$x/y$".

Solution:

• The given scales can be expressed as ratios.
• Scale of the first map in ratio form is expressed as $1cm/20km$.
• Scale of the second map in ratio form is expressed as $1cm/100km$.
• The distance from Fresno to San Francisco in the first map is $15cm$.
• The distance from Fresno to San Fracisco in second map is different from that of the first map, due to the change of scale.
• Let '$x$' be the distance on second map and that distance in second map is calculated in the following way:

$1/20$ - $15$

$1/100$ - $x$

Using cross multiplication,

$(1/20)x=(1/100)15\\(1/20)x=15/100\\x=(15/100)*(20/1)\\x=15/5\\x=3$

⇒The required distance is $3cm$

Final Answer:

∴The distance from Fresno to San Francisco on the second map is $3cm$.

Answer 2

Answer:

Given:

There are two different maps for California.

Scale of the first map is \begin{gathered}1cm to 20km\\\end{gathered}

1cmto20km

.

Distance between Fresno and San Francisco = \begin{gathered}15cm\\\end{gathered}

15cm

Scale of the second map is \begin{gathered}1cm to 100km\\\end{gathered}

1cmto100km

To find:

The distance between from Fresno to San Francisco according to the second map.

Note:

Any scale of '\begin{gathered}x\\\end{gathered}

x

' cm to '\begin{gathered}y\\\end{gathered}

y

' km can be expressed in the ratio form which is given by "\begin{gathered}x/y\\\end{gathered}

x/y

".

Solution:

The given scales can be expressed as ratios.

Scale of the first map in ratio form is expressed as \begin{gathered}1cm/20km\\\end{gathered}

1cm/20km

.

Scale of the second map in ratio form is expressed as \begin{gathered}1cm/100km\\\end{gathered}

1cm/100km

.

The distance from Fresno to San Francisco in the first map is \begin{gathered}15cm\\\end{gathered}

15cm

.

The distance from Fresno to San Fracisco in second map is different from that of the first map, due to the change of scale.

Let '\begin{gathered}x\\\end{gathered}

x

' be the distance on second map and that distance in second map is calculated in the following way:

\begin{gathered}1/20\\\end{gathered}

1/20

- \begin{gathered}15\\\end{gathered}

15

\begin{gathered}1/100\\\end{gathered}

1/100

- \begin{gathered}x\\\end{gathered}

x

Using cross multiplication,

\begin{gathered}(1/20)x=(1/100)15\\(1/20)x=15/100\\x=(15/100)*(20/1)\\x=15/5\\x=3\\\end{gathered}

(1/20)x=(1/100)15

(1/20)x=15/100

x=(15/100)∗(20/1)

x=15/5

x=3

⇒The required distance is \begin{gathered}3cm\\\end{gathered}

3cm

Final Answer:

∴The distance from Fresno to San Francisco on the second map is \begin{gathered}3cm\\\end{gathered}

3cm

.