SOLUTION: John and Bob can clean the house in 3 hours. If each work alone, it would take Bob one hour longer to clean the house than it would take John. How long would it take Bob to clean t

Question 1009210: John and Bob can clean the house in 3 hours. If each work alone, it would take Bob one hour longer to clean the house than it would take John. How long would it take Bob to clean the house alone?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Bob to clean the house
Then Bob works at the rate of 1/x house per hour
John cleans the house in x-1 hours
So John cleans at the rate of 1/(x-1) house per hour
Together they clean at the rate of 1/3 house per hour
sooo
1/x +1/(x-1)= 1/3 multiply each term by 3x(x-1)
3(x-1)+3x=x(x-1)
3x-3+3x=x^2-x
x^2-7x+3=0
solve using quadratic formula and we get
x=~6.54 hrs and
x=~0.46 hrs---this cannot be correct. Can't have John cleaning in negative hours.
So the answer is x~=6.54 hours---time it takes Bob
Then 5.54 hours----time it takes John
CK
1/6.54 + 1/5.54 =1/3
0.1529 + 0.1805=0.3333
0.3334~~~~~0.3333
Hope this helps--ptaylor

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