SOLUTION: Dal and Kim can assemble a swing set in 1 and 1/2 hours. Working alone it takes Kim 4 hours longer than Dal to assemble the swing set. How long would it take Dal, working alone, to

Question 366864: Dal and Kim can assemble a swing set in 1 and 1/2 hours. Working alone it takes Kim 4 hours longer than Dal to assemble the swing set. How long would it take Dal, working alone, to assemble the swing set? I have tried everything I could to solve this one and haven't had any luck. I would appreciate anyone's help! Thank you for your time!
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Dal to assemble the swing set, working alone
Then Dal works at the rate of 1/x swing set per hour
We are told that it takes Kim 4 hours longer than Dal, so it must take Kim x+4 hours to assemble the set
Then Kim works at the rate of 1/(x+4) swing set per hour
We are also told that Dal and Kim work at the rate of 1/(1.5) swing set per hour
Then our equation to solve is:
1/x + 1/(x+4)=1/(1.5) Multiply each term by 1.5(x)(x+4)
1.5(x+4)+1.5x=x(x+4) get rid of parens
1.5x+6+1.5x=x^2+4x simplify
x^2+x-6=0-----quadratic in standard form and it can be factored:
(x+3)(x-2)=0
x=2 hrs-------ANS--Time it takes Dal working alone
x=-3 NO! time in this prob is positive
CK
In 1.5 hours, Kim completes (1/6)(1.5)=(1.5)/6 of the swing set
In 1.5 hours, Dal completes (1/2)(1.5)=(1.5)/2 of the swing set
(1.5)/6+(4.5)/6=6/6=1 (swing set, that is)
Hope this helps---ptaylor

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