Question

a dog barks every 10 minutes a cat miaows every 12 minutes when will they bark and miaow together

Answer 1

THE TIME AT WHICH THE DOG WILL BARK AND THE CAT WILL MIAOW TOGATHER WILL BE EQUAL TO THE LCM OF THE TIME THEY TAKE FOR EVERY BARK AND MIAOW

THUS LCM OF 10 AND 12

WHICH IS EQUAL TO 60 MINS

THSI THE DOG WILL BARK AND THE CAT WILL MIAOW TOGATHER AFTER 60 MIN

Answer 2

Given,

A dog barks after every 10 minutes.

A cat miaows after every 12 minutes.

To find,

The time when they both will bark and miaow together.

Solution,

The time when they both will bark and miaow together will be after 60 minutes.

We can easily solve this problem by following the given steps.

According to the question,

A dog barks after every 10 minutes.

A cat miaows after every 12 minutes.

To find the time when they will both bark and miaow together, we will have to find the Lowest Common Multiple (LCM) of 10 and 12.

Using the prime factorization method, we have

10 = 2×5

12 = 2×2×3

Then, the LCM of 10 and 12 is (2×2×3×5) which is 60.

So, they will both bark and miaow together after 60 minutes.

(60 minutes make an hour. So, it can also be said to be after 1 hour.)

Hence, the time when they both will bark and miaow together is after 60 minutes ( or 1 hour).