Question

It takes four workers six hours and 45 minutes to plant 24 trees. If the time it takes to plant trees varies directly with the number of trees and inversely with the number of workers, how many trees could 9 workers plant in four and a half hours?​

Answer 1

36 trees

Explanation:

We are told that It takes four workers six hours and 45 minutes to plant 24 trees. Also that the time it takes to plant trees varies directly with the number of trees and inversely with the number of workers.

Thus,

t ∝ x/n

Where;

x is number of trees

n is number of workers

Now, opening the proportion symbol, we have;

t = kx/n

Where k is the constant of proportionality.

t = 6 hours 45 minutes = 6¾ hours = 6.75 hours

Plugging in the relevant values, we have;

6.75 = 24k/4

k = 4 × 6.75/24

k = 1.125

Now, we want to know how many trees could 9 workers plant in four and a half hours (4.5 hours)

Applying the same as above and Plugging in k = 1.125, we have;

4.5 = 1.125x/9

x = 9 × 4.5/1.125

x = 36 trees