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