Answer:
12 minutes
Step-by-step explanation:
We must understand that as the number of people increase in a work, lesser time is taken to finish the work. This implies that the number of people is inversely proportional to the time taken to do the work.
Let n be the number of people.
Let t be the time taken to do the work.
Thus,
n ∝ 1/t
n = K/t
Next, we shall determine the constant of proportionality. This can be obtained as follow:
Number of people (n) = 2
Time (t) = 1 h = 60 minutes
Constant of proportionality (K) =.?
n = K/t
2 = K / 60
Cross multiply
K = 2 × 60
K = 120
Finally, we shall determine the time taken for 10 people to do the work. This can be obtained as follow:
Number of people (n) = 10
Constant of proportionality (K) = 120
Time (t) = ?
n = K/t
10 = 120 / t
Cross multiply
10 × t = 120
Divide both side by 10
t = 120 / 10
t = 12 minutes
Thus, it will take 12 minutes for 10 people to finish the work.
