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Thread: Need help in Ratios

  1. #1
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    Need help in Ratios

    Q#1
    Building hallway is 23.5 inches long.
    The scale is 3.25 inches = 14 feet. How long is the hallway??


    Q#2
    Drawing with a scale of 3.75 inches = 13 feet. What distance on the drawing should be used to represent 9 feet 3 inches??


    Q#3
    On level ground, a street pole casts a shadow 10.7 m long. At the same time, a tree 25.0 m high casts a shadon 35.0 m long. How high is the pole?
    I tried this, but my number is way to small.


    Q#4
    On a map, 8cm = 50 km. What is the distance between the two cities if the distance between them on the map is 13.6cm.
    Actual distance in km??


    Thanks for your help, and explain fully so I can understand.
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  2. #2
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    Ratios and multiplying factors

    Hello bradycat
    Quote Originally Posted by bradycat View Post
    Q#1
    Building hallway is 23.5 inches long.
    The scale is 3.25 inches = 14 feet. How long is the hallway??


    Q#2
    Drawing with a scale of 3.75 inches = 13 feet. What distance on the drawing should be used to represent 9 feet 3 inches??


    Q#3
    On level ground, a street pole casts a shadow 10.7 m long. At the same time, a tree 25.0 m high casts a shadon 35.0 m long. How high is the pole?
    I tried this, but my number is way to small.


    Q#4
    On a map, 8cm = 50 km. What is the distance between the two cities if the distance between them on the map is 13.6cm.
    Actual distance in km??


    Thanks for your help, and explain fully so I can understand.
    There are two important things that you need to learn to do when dealing with maps and plans. They are:

    First, in questions like this, change the scale that you've been given so that both bits are in the same units. So, for instance, in #1 the scale you're given is:
    $\displaystyle 3.25$ inches represents $\displaystyle 14$ feet
    So that's:
    $\displaystyle 3.25$ inches represents $\displaystyle 14 \times 12 = 168$ inches
    That's a ratio of:
    $\displaystyle 3.25 : 168$
    Noting that $\displaystyle 0.25$ is one-quarter, multiply both numbers in the ratio by $\displaystyle 4$ to get rid of decimals. That's:
    $\displaystyle 3.25 \color{red}\times 4\color{black}:168\color{red}\times 4$
    $\displaystyle = 13:672$
    This means that $\displaystyle 13$ inches (or feet, or whatever) on the plan represents $\displaystyle 672$ inches (feet, whatever) on the ground.

    Secondly, learn how to make things bigger and smaller using what are called multiplying factors. It's very simple. If you have a ratio
    $\displaystyle A:B$
    then the multiplying factors are:
    $\displaystyle \frac AB$ and $\displaystyle \frac BA$
    That's all. There aren't any more.

    So with the ratio
    $\displaystyle 13:672$
    the multiplying factors are
    $\displaystyle \frac{13}{672}$ and $\displaystyle \frac{672}{13}$
    And then all you need to know is, to make a number bigger, use the multiplying factor that has the bigger number on top; to make a number smaller use the one that has the smaller number on top.

    OK. Now I'll complete question #1, and see if you can do the others. As we've said, the multiplying factors are:
    $\displaystyle \frac{13}{672}$ and $\displaystyle \frac{672}{13}$
    On the plan, the hallway is $\displaystyle 23.5$ inches. Obviously the real hallway is much bigger than this. So we multiply $\displaystyle 23.5$ inches by $\displaystyle \frac{672}{13}$. And the answer is:
    $\displaystyle 23.5\times \frac{672}{13}$
    $\displaystyle =1215$ inches (to the nearest inch)

    $\displaystyle = 101$ feet $\displaystyle 3$ inches
    Now have a go at the others. Let us know if you get stuck.

    Grandad
    Last edited by Grandad; Mar 1st 2010 at 12:14 AM. Reason: Corrected typo
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