SOLUTION: a woman asked 10 boys to clean a 5 roomed house, they finished it in 30 minutes. How long will it take 15 boys to finish cleaning the house????

Question 898136: a woman asked 10 boys to clean a 5 roomed house, they finished it in 30 minutes. How long will it take 15 boys to finish cleaning the house????

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

RELATED QUESTIONS
Gently can clean the house in 1 Hour and 40 minutes while marivic can clean the house in... (answered by josgarithmetic)

melissa can clean the house in 4hours, whereas her husband, zack, can do the same job in... (answered by ankor@dixie-net.com)

three man can finish a painting job in 8 days. This job can be finished by 5 women in 6... (answered by ankor@dixie-net.com)

If 4 boys can clean the gymnasium in 2 hours, how many minutes will it take 5 boys to do... (answered by mananth)

20 men or 30 boys can do a certain job in 20 days. how long will it take 6 men and 15... (answered by ankor@dixie-net.com)

If 6 men can harvest a field in 60 working hours, and a man works three times as fast as... (answered by Theo)

If 4 men clean a house in 150 minutes, how long will it take 5 men to complete the same... (answered by stanbon)

If your friend take 5 hours longer to clean a house and together it takes 6 hours. How... (answered by ankor@dixie-net.com)

3 boys are working on a school project. Joseph and Bill can finish the prohectbin 10... (answered by josgarithmetic,greenestamps)