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.

This comment has been removed by the author.

ReplyDeleteMethod 1:

ReplyDeleteDog - 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

Method 1:

ReplyDeleteTotal 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

Method 1:

ReplyDeleteDistance 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

First Method:

ReplyDelete3 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

1)

ReplyDelete30x3=90

90 divided by 4+22.5

22.5x12=270

2)

3 divided by 4=3/4

3/4x30=22.5

22.5x12=270

Method 1:

ReplyDelete30x3=90

90x3=270#

Method 2:

30/4=7.5

7.5x12=270#

method 1:

ReplyDelete30x3=90

12/4=3

90x3=270

method 2:

3steps(dog) : 4 steps (cat)

9 steps(dog) : 12 steps (cat)

9x30=270

Method 1:

ReplyDelete3steps of dog : 4 steps of cat

9steps of dog : 12 steps of cat ##

Method 2:

30x3=90

12÷4=3

90x3=270

This comment has been removed by the author.

ReplyDeleteMethod 1:

ReplyDelete30x3=90cm

1 cat step: 90/4=22.5cm

12 cat steps: 22.5x12=270cm

Method 2:

dog:cat

3 : 4

9 : 12

9x30=270cm

Method 1:

ReplyDeleteThe 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

@siddharth @Ben

ReplyDeleteDo read through the questions more carefully.

Maybe a diagram might be helpful :)

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

ReplyDeleteAmongst 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.

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

ReplyDeleteStep 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.

Ist Method

ReplyDelete3*30=90

90/4=22.5

22.5*12=270

2nd Method

Dog:Cat

3:4

9:12

90*3=270