Answer:
[tex]\frac{b}{a}[/tex] is the total time taken to clean the house.
Step-by-step explanation:
Given that:
Betsy cleans [tex]\frac{a}{b}[/tex] 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 [tex]\frac{a}{b}[/tex] 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 [tex]\frac{a}{b}[/tex].
Now, Let us solve this mathematically:
[tex]\frac{a}{b}[/tex] of the house is cleaned in = 1 hour
1 of the house will be cleaned in = 1 hour divided by [tex]\frac{a}{b}[/tex]
[tex]\dfrac{1}{\dfrac{a}{b}}\ hours\\\Rightarrow \dfrac{1 \times b}{a}\ hours\\\Rightarrow \dfrac{b}{a}\ hours[/tex]
So, the answer is:
[tex]\frac{b}{a}[/tex] is the total time taken to clean the house.
