SOLUTION: This is a problem using quadratic equations. I am really confused. I would appreciate your help. Three girls Laura, Tammy, and Jeri can wash the family car, clean the pool, a

Question 192678: This is a problem using quadratic equations. I am really confused. I would appreciate your help.
Three girls Laura, Tammy, and Jeri can wash the family car, clean the pool, and mow the lawn in 1 hour and 20 minutes. If Jeri did the work she would take twice as long as Tammy + 2 hours longer than Laura. How long would each girl take?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let x represent the number of hours that Tammy would take, then 2x is the number of hours that Jeri would take, and 2x - 2 is the number of hours that Laura would take.

Since they took 1 hour and 20 minutes

, they can do

of the job in 1 hour.

Tammy can do

of the job in 1 hour.

Jeri can do

of the job in 1 hour.

Laura can do

of the job in 1 hour.

So, together they can do:

The LCD is

, so:

Combining like terms:

Multiply by

, making a note to exclude the values of 0 and 1 from the ultimate solution set because these values would make the denominator = zero.

Which factors:

Meaning that Tammy would take either

of an hour or 3 hours to do the job. The

answer is an absurdity because that would mean that Jeri could do the job in

which is the time that it took all three to actually do it. Exclude

as an extraneous root. The correct answer is then 3 hours for Tammy, two times that, or 6 hours for Jeri, and two hours less than that, or 4 hours for Laura.

Check:

.

So they can do three-fourths of the job in 1 hour, or the whole job in the reciprocal of that, or four-thirds hour which is 1 hour and 20 minutes.

John

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