Answer:
A. 54 minutes
Step-by-step explanation:
Given that:
Number of people working together to clean = 3
Time taken for cleaning when 3 people are working = 90 minutes
To find:
If the number of people are increased to 5, what will be the total time taken ?
Solution:
Formula for Total work is given as following:
Total work = Total men working multiplied with Time for which they work.
i.e.
[tex]W = M \times T[/tex]
Here, we are given two situations:
[tex]M_1[/tex] = 3
[tex]T_1[/tex] = 90 minutes
[tex]M_2[/tex] = 5
[tex]T_2[/tex] = ?
Here, Total work in the two situations is same.
i.e. [tex]W_1 = W_2[/tex]
[tex]3\times 90 = 5 \times T_2\\\Rightarrow T_2 = \dfrac{270}{5}\\\Rightarrow \bold{T_2 = 54\ min}[/tex]
Therefore, the answer is:
A. 54 minutes
The time taken for 5 people to clean the same house working at the same rate is 54 minutes.
The given parameters:
The time taken for 5 people to clean the same house working at the same rate is calculated as follows.
[tex]no . \ of \ people = \frac{k}{t} \\\\n = \frac{k}{t} \\\\k = nt\\\\n_1 t_1 = n_2t_2[/tex]
where;
n₁ = 3 people
n₂ = 5 people
t₁ = 90 mins
t₂ = ?
[tex]t_2 = \frac{n_1t_1}{n_2} \\\\t_2 = \frac{3 \times 90 \min}{5} \\\\t_2 = 54 \min[/tex]
Thus, the time taken for 5 people to clean the same house working at the same rate is 54 minutes.
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