Rate problem making me crazy!

[MedHopeful234]

I'm going crazy...

Can someone PLEASE tell me how in the world destroyer did this problem? I just can't seem to understand why they multiplied/divided the way they did to get the rate....

If it takes 5 people 12 hours to paint 3 identical houses, then how many hours will it take 4 people working at the same rate to paint 5 houses?

How I did it: 12 hours/ 3 houses....= 4 hours per house, 5 people worked so 5 people/4hr/hs...which would be the same as 5 people * 1 house/4 hours

with 4 people working to paint 5 houses, that would be 4 hr / (5ppl*hs) (I just flipped the final rate)... x 4 people x 4 houses... giving me 16 hours....


According to destroyer, it will take one person 60 hours to paint 3 houses and 20 hours to paint 1 house... and therefore it will take 4 people 5 hours to paint one house and 25 hours to paint 5 houses

But I don't understand the logic here because it specifically says that FIVE people take 12 hours... not each person takes 12 hours....

Please help... I'm going crazyyyyyy 😕😕😕

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[Pillowcases]

5 people 4 hours 1 house, so 1 person would take 20 hours
In 1 hour, a person would complete 1/20 part of the house << this is the essential info you need to understand the problem
4 people would complete 4/20 parts in 1 hour (1 house), so it would take them 25 hours to complete 100/100 parts (5 houses)

 

[StumpMT]

^ This.

I solved it by using a slightly different method. From 5 people can paint 1 house in 4 hours you can see that it takes 1 person 5 times longer to accomplish the same task ie 1 person can paint 1 house in 20 hours. Two times the people can accomplish the same task in half the time ie you divide the hours taken by 2, etc. So if you multiply the number of people painting by 4 then you need to divide the number of hours taken by 4, which would give you 5 hours for 1 house. Then just multiply that by the number of houses you need and you have your answer.

 

[MedHopeful234]

Thank you guys so much! it makes so much sense now. For some reason I get so nervous and over think these problems

 

[Pillowcases]

Don't worry about it, the real DAT isn't this complex \(^-^)/