### 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.

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

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

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

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

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

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

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)

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

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

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.

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

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

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)

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.

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

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

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

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