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.

1. cat 4 steps= 3*30

ReplyDelete= 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

Method 1-->

ReplyDeleteDog:

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

Method 1: 3 steps of dog=90cm=4 steps of cat

ReplyDelete12 steps of cat=90cmx3=270cm

Method 2: 3:4

9:12

Dog 9 steps= 30cmx9=Cat 12 steps=270cm

Method 1:

ReplyDelete3 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

Method 1

ReplyDelete3 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

Method 1:

ReplyDeleteFind 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

Method 1:

ReplyDelete3 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)

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?

ReplyDeleteMethod 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

1.Let us take Dog's Steps as D and Cat's Steps as C.

ReplyDelete3D=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

1. Let Dog's steps be D and cat's step be C.

ReplyDeleteAs 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.

1.

ReplyDelete30cmx3=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

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

ReplyDelete2. 3*30=90cm

4 steps = 90cm

1 step = 90cm/4

= 22.5cm

12 steps = 22.5cm*12

= 270cm

Gladys

METHOD ONE:

ReplyDeletedist = 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)

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

ReplyDeleteIndeed, 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.

Method 1: Dog= 3 steps/90cm

ReplyDeleteCat= 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

1) Dog 3 steps = Cat 4 steps

ReplyDelete= 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

Method 1 :

ReplyDeleteDog 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

1.

ReplyDeleteCat'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