### 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.

1. This comment has been removed by the author.

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

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

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

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

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

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

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

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

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

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

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

10. This comment has been removed by the author.

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

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

13. @siddharth @Ben

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

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.

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.

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