Question 898136
rate per person times number of people times time = quantity
r*p*t = q


quantity is 1 clean house.
t = 30 minutes
p = 10
you are solving for rate per person.


formula becomes:


r*10*30 = 1


divide both sides of the equation by 10*30 to get:


r = 1 / (10 * 30) = 1/300.


1 person can clean 1/300 of the house in 1 minute.


1/300 * 10 * 30 = 300 / 300 = 1 cleaned house, so the value of r is confirmed to be good.


r is the amount of the house tht 1 person can clean in one minute.


you have established that one person can clean 1/300 of the house in 1 minute.


now you want to know how long it would take 15 persons to clean the house.


the formula of r*p*t = q is used again, and becomes:


(1/300) * 15 * t = 1


now you want to solve for t.


you get t = (1 / 15) * 300 = 20 minutes.


10 boys can clean the house in 30 minutes.
15 boys can clean the house in 20 minutes, working at the same rate for each boy.


1/300 * 10 * 30 = 1


1/300 * 15 * 20 = 1


solution is it will take 15 boys 20 minutes to clean the house.