Question

2 people can paint a fence in one hour. How long would it take 10 people? Please answer in minutes :)

Answer 1

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.