6AM Quiz (2011, June 18): It's about cats and dogs

A dog takes 3 steps to walk the same distance for which the cat takes 4 steps. Suppose 1 step of the dog covers 30 cm. How many centimeters would the cat cover in taking 12 steps?

There are at least 2 methods to solve the above problem.
Describe any 2 methods that leads to the answer.

16 comments:

  1. This comment has been removed by the author.

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  2. Method 1:
    Dog - 3 Steps = Cat - 4 Steps
    3 Steps(Dog) = 30 X 3 = 90
    90 cm = 3 Steps(Dog) / 4 Steps(Cat)
    90 / 4 = 22.5 cm
    1 Step(Cat) = 22.5 cm
    12 Steps(Cat) = 270 cm Ans: 270 cm

    Method 2:
    12 / 4 = 3 ( 3 groups of 4 = 12)( 3 and 4 is divisible by 12)
    30 X 3 = 90
    90 X 3 = 270 cm Ans: 270 cm

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  3. Method 1:
    Total distance covered: 3 X 30 = 90
    90/4 = 22.5
    1 Step for the cat is 22.5cm
    12 steps = 22.5cm X 12 = 270 cm
    Answer: 270cm

    Method 2:
    12/4 = 3
    That means that 12 steps would be 3 times the distance taken by 3 steps of the dog.
    30 X 3 = 90
    90 X 3 = 270
    Answer: 270

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  4. Method 1:
    Distance covered by dog in 3 steps:
    3x30cm=90cm
    3 dog steps=4 cat steps=90cm

    12 cat steps:
    90cmx3=270cm

    Method 2:
    3 dog steps=4 cat steps
    3 dog steps=3x30cm=90cm
    90cm/4=22.5cm
    22.5cmx12=270

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  5. First Method:
    3 steps of the dog is:
    3x30=90
    12 steps of the cat=9 steps of the dog
    12 steps of the cat is:
    90x(9/3)=270
    Answer: 270cm

    Second Method:
    3 steps of the dog is: 90
    1 step of the cat is:
    90/4=22.5
    12 steps of the cat is:
    22.5x12=270
    Answer: 270cm

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  6. 1)
    30x3=90
    90 divided by 4+22.5
    22.5x12=270
    2)
    3 divided by 4=3/4
    3/4x30=22.5
    22.5x12=270

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  7. Method 1:
    30x3=90
    90x3=270#

    Method 2:
    30/4=7.5
    7.5x12=270#

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  8. method 1:
    30x3=90
    12/4=3
    90x3=270

    method 2:
    3steps(dog) : 4 steps (cat)
    9 steps(dog) : 12 steps (cat)

    9x30=270

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  9. Method 1:

    3steps of dog : 4 steps of cat
    9steps of dog : 12 steps of cat ##

    Method 2:

    30x3=90
    12÷4=3
    90x3=270

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  10. This comment has been removed by the author.

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  11. Method 1:
    30x3=90cm
    1 cat step: 90/4=22.5cm
    12 cat steps: 22.5x12=270cm

    Method 2:
    dog:cat
    3 : 4
    9 : 12
    9x30=270cm

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  12. Method 1:
    The first step is to find out what is the distance the dog walks for 3 steps
    30cm x 3 steps(d)=90cm

    90cm is the distance which the cat walks if it take 4 steps, so we take the total distance and divide it by 4 steps(c)
    90/4=22.5cm

    After that we multiply the 22.5cm with 12 steps.
    22.5cm x 12 steps=270cm

    Method 2:

    3D(3 steps of dog) = 4C(4 steps of cat)
    D=4/3 C
    30cm= 4/3 C
    30cm/ 4/3 =C
    30cm x 3/4 =C
    22.5cm=C
    22.5 x 12 = 270cm

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  13. @siddharth @Ben

    Do read through the questions more carefully.
    Maybe a diagram might be helpful :)

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  14. The rest of you... your answers are correct :)

    Amongst all the correct answers, Jia En's description of thinking was most comprehensive as she had explained her thought processes clearly.
    Well done, Jia En.

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  15. Here's one suggestion how I would explain the method using proportion:

    Step 1: Find out how many dog steps are equivalent to 12 cat steps. [This is using Proportion]

    Since 4 cat steps is equivalent to 3 dog steps,
    Then 12 cat steps is equivalent to (3x3) dog steps.

    Step 2: Find out total steps covered in 9 dog steps.

    Distance covered by 1 dog step = 30 cm
    Distance covered by 9 dog steps = 30x9 cm = 270 cm

    Therefore, the cat will cover 270 cm in 12 steps.

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  16. Ist Method
    3*30=90
    90/4=22.5
    22.5*12=270

    2nd Method
    Dog:Cat
    3:4
    9:12
    90*3=270

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