6AM Quiz (2011, 18 June): 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.

18 comments:

  1. 1. cat 4 steps= 3*30
    = 90cm
    cat 12 steps=90*3
    =270cm
    2. dog:cat
    3 : 4 *3
    9 : 12
    cat 12 steps=dog 9 steps
    cat 12 steps=30*9
    =270cm

    ReplyDelete
  2. Method 1-->
    Dog:
    1 step: 30cm
    3 steps: 30cm*3=90cm

    Cat:
    4 steps: 90cm
    12 steps: 90cm*3=270cm

    Method 2-->
    Lets say the the distance 1 step of the dog covers is: x
    Lets say the the distance 1 step of the cat covers is: y

    3x=4y
    3x/1=4x/1
    Ratio of the distance 1 step of the dog covers to the distance 1 step of the cat covers: 4:3

    4 units:30 cm
    1 unit: 30/4 cm
    3 units: 30/4*3=90/4

    12 steps of cat: 90/4*12=270

    ReplyDelete
  3. Method 1: 3 steps of dog=90cm=4 steps of cat
    12 steps of cat=90cmx3=270cm

    Method 2: 3:4
    9:12
    Dog 9 steps= 30cmx9=Cat 12 steps=270cm

    ReplyDelete
  4. Method 1:
    3 x 30cm= 90cm ( 4 steps of the cat)
    90cm x 3= 270cm ( 12 steps of the cat)

    Method 2:
    Let each step the dog takes be x
    Let each step the cat takes be y
    3x=4y
    x=30cm
    3x=90cm
    90cm=4y
    12y=270cm

    ReplyDelete
  5. Method 1

    3 x 30cm=90cm
    1 step for a cat--->90cm÷4=22.5cm
    12 steps--->22.5cm x 12= 270cm

    Ans: 270cm

    Method 2

    Let a step that a dog takes be d; and a step that a cat takes be c.

    3d=4c

    3d=3 x 30
    3d=90

    4c=90
    12c÷4c=3
    12c=90 x 3= 270

    Ans: 270cm

    ReplyDelete
  6. Method 1:

    Find the distance the dog and cat had covered: 3*30cm=90cm

    Find the distance covered by the cat with one step : 90cm/4=22.5cm

    Find the distance covered by the cat with 12 steps: 22.5cm*12=270cm

    Ans:270cm

    Method 2:
    let the cat be x.
    Let the dog be y.

    4x=3y

    3y=3(30)
    3y=90

    4x=90
    4x/4=90/4
    x=22.5

    12(x)=12x(distance covered by cat with 12 steps)
    12x=12(22.5)
    12x=270cm

    Ans : 270cm

    ReplyDelete
  7. Method 1:
    3 Dog steps= 4 cat steps
    1dog step->30 cm
    3 dog steps->30cm*3=90cm
    3 dog steps= 4 cat steps
    ∴ 4 cat steps->90cm
    1 cat step->90cm÷4=22.5cm
    12 cat steps->22.5cm*12=270cm(ANS)

    Method 2:
    Let each step of the cat be c.
    Let each step of the dog be d.
    d=30cm
    3d=3(30)
    =90cm
    ∵3d=4c,
    4c=90cm
    c=90cm÷4
    =22.5cm
    12c=22.5(12)
    =270cm(ANS)

    ReplyDelete
  8. 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?

    Method 1:
    1 step of dog = 30cm
    3 steps = 90cm
    3 steps of dog = 4 steps of cat
    4 steps of cat = 90cm
    12 steps of cat = 270cm

    Method 2:
    Let each step of the dog be x.
    Let each step of the cat be y.
    x = 30cm
    3x = 30cm*3
    = 90cm
    3x = 4y
    4y = 90cm
    12y = 90cm*3
    = 270cm

    ReplyDelete
  9. 1.Let us take Dog's Steps as D and Cat's Steps as C.
    3D=4C
    1D=30cm
    3D=90cm
    4C=90cm
    12C=270cm

    The Cat's steps is 3/4 of the dog's steps
    One dog's step=30cm
    12 dog's steps=360cm
    12 cat's steps= 360÷4x3
    = 270cm

    ReplyDelete
  10. 1. Let Dog's steps be D and cat's step be C.
    As 3 dog's steps equals to 4 cat's steps, so 3D=4C.
    D=30

    3D=30x3
    =90

    3D=90
    3D=4C
    4C=90
    Thus, 12C=90x3
    =270cm

    2. The answer requires 12 steps of the cat so by the information that 3 steps of a dog -> 4 steps of a cat.
    So to make it a ratio, it would be 3:4
    To make the 4 into 12, we have to multiply it by 3. Same for the dog's steps. So..... 3x3:4x3 = 9:12

    Length of 12 cat's steps is 9x30 = 270cm

    Owen here.

    ReplyDelete
  11. 1.
    30cmx3=90cm (3 dog steps)

    12÷4=3 (*No. of 3 dog steps)

    3x90cm=270cm (12 cat steps)

    ANS:270cm

    2.
    30cmx3=90cm (3 dog steps)

    90cm÷4=22.5cm (1 cat step)

    22.5cmx12=270 (12 cat steps)

    ANS:270cm

    ReplyDelete
  12. 1. Dog can travel 30cm*3=90cm in 3 steps, while cat can travel 90cm in 4 steps. The cat needs to travel 3 times in order to travel 12 steps. So 90cm*3=270cm

    2. 3*30=90cm
    4 steps = 90cm
    1 step = 90cm/4
    = 22.5cm
    12 steps = 22.5cm*12
    = 270cm

    Gladys

    ReplyDelete
  13. METHOD ONE:
    dist = 3 x 30
    = 90

    1 step (cat) = 90 ÷ 4
    = 22.5

    12 steps = 22.5 x 12
    = 270 cm


    METHOD TWO:
    3 dog steps => 90cm
    4 cat steps => 90cm

    as (4 cat steps = 3 dog steps)

    4 cat steps => 90cm
    12 cat steps => ? cm

    distance travelled by 12 cat steps
    = (12/4) * 90
    = 3 * 90
    = 270cm

    Toby Gail (06)

    ReplyDelete
  14. Interesting to see that a number of you attempted the question using Algebra.

    Indeed, all of you had covered the method which required us to find the 'unit length' covered the cat, then multiply accordingly.

    A number of you attempted to use 'ratio' in the working, which is also a good attempt. For that, the steps/ thinking has to be explained further.

    Here's another suggestion (how to explain the solution). This is close to the ratio method, actually:

    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.

    ReplyDelete
  15. Method 1: Dog= 3 steps/90cm
    Cat= 4steps/90cm
    12/4=3
    3x90cm=270cm

    Method 2: Ratio of dog to cat steps= 3:4
    = 9:12
    1 unit= 30cm
    A dog covers 9 steps which is equivalent to 12 steps of the cat
    30cm x 9 = 270cm
    270cm which is 9 steps of the dog is the same as 12 steps of the cat

    ReplyDelete
  16. 1) Dog 3 steps = Cat 4 steps
    = 90cm
    12/4 = 3
    3x90cm= 270cm

    2) Ratio of dog steps to cat steps= 3:4
    = 9:12
    1 dog step unit = 30cm
    9 dog steps = 12 cat steps = 270cm

    ReplyDelete
  17. Method 1 :
    Dog 3 steps = 30*3 cm
    = 90 cm
    Cat 12 steps = 90*3
    = 270 cm

    Method 2 :
    Dog's step : Cat's step = 3:4
    = 9:12
    1 dog's step = 30 cm
    3 dog's step = 4 cat's step
    9 dog's step = 12 cat's step
    = 270 cm

    ReplyDelete
  18. 1.
    Cat's Speed is 3/4 of Dog's Speed.
    So Cat will cover 3/4 of the Dog's distance in the same amount of time/unit.
    3/4*30=22.5
    Cat's Speed:
    22.5 cm/step
    270 cm/12 steps

    2.
    12/4=3
    3*3=9
    9 steps of Dog is same as 12 steps of Cat.
    9*30cm=270cm

    Ans:270cm

    ReplyDelete