Question

Betsy can clean a b of the house in an hour. How long will it take her to clean the whole house?

Answer 1

`(b)/(a)` is the total time taken to clean the house.

Explanation:

Given that:

Betsy cleans
`(a)/(b)` of the house.

Time taken = 1 hour

To find:

Time taken to clean the whole house = ?

Solution:

We can use unitary method here to solve this problem.

We are given that
`(a)/(b)` of the house is cleaned in 1 hour.

We have to find that a total of 1 house will be cleaned in how much time.

(1 house because Betsy's house can be considered as a single unit).

To find this we will divide 1 hour with
`(a)/(b)`.

Now, Let us solve this mathematically:

`(a)/(b)` of the house is cleaned in = 1 hour

1 of the house will be cleaned in = 1 hour divided by
`(a)/(b)`

`(1)/((a)/(b))\ hours\\\Rightarrow (1 * b)/(a)\ hours\\\Rightarrow (b)/(a)\ hours`

So, the answer is:

`(b)/(a)` is the total time taken to clean the house.