SOLUTION: Jerry can lay a tile floor in 3 hours less time than Jake. If they can work together, the floor takes 2 hours. How long would it take Jerry to lay the floor by himself?

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Question 997068: Jerry can lay a tile floor in 3 hours less time than Jake. If they can work together, the floor takes 2 hours. How long would it take Jerry to lay the floor by himself?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
rate * time = quantity of work.

quantity of work = 1 job

jerry can lay a tile floor in 3 hours less time than jake.

let x = the amount of time that jake takes.
then x - 3 = the amount of time that jerry takes.

since rate * time = quantity, then:

for jake, rate * time = quantity becomes rate * x = 1

for jerry, rate * time = quantity becomes rate * (x-3) = 1

solve for rate in each of these equations and you get:

for jake, rate = 1/x

for jerry, rate = 1/(x-3)

when they work together, they can do the job in 2 hours.

their rates are additive when they work together.

time is equal to 2 hours.
quanity is still equal to 1 job.

rate * time = quantity becomes:

(1/x + 1/(x-3) * 2 = 1

you want to solve for x.

remove the parentheses to get:

2/x + 2/(x-3) = 1

multiply both sides of the equation by x * (x-3) to get:

(2 * x * (x-3) / x + (2 * x * (x-3)) / (x-3) = 1 * x * (x-3)

simplify to get:

2 * (x-3) + 2 * x = x * (x-3)

remove parentheses to get:

2 * x - 6 + 2 * x = x^2 - 3 * x

combine like terms to get:

4 * x - 6 = x^2 - 3 * x

subtract 4 * x from both sides of the equation and add 6 to both sides of the equation to get:

0 = x^2 - 7 * x + 6

solve for the factors of this quadratic equation to get:

(x - 6) * (x - 1) = 0

solve for x to get:

x = 6 or x = 1

x can't be equal to 1 because then x - 3 would be negative and negative values of time or rate are not allowed.

x has to be equal to 6 or not at all.

to confirm that x = 6 is good, go back to the original equation where they were both working together to get:

(1/x + 1/(x-3) * 2 = 1 becomes:

(1/6 + 1/(6-3)) * 2 = 1 which becomes:

(1/6 + 1/3) * 2 = 1 which becomes:

(1/6 + 2/6) * 2 = 1 which becomes:

3/6 * 2 = 1 which is equal to 1/2 * 2 = 1 which is equal to 1 = 1.

this confirms the value of x is good.

you are asked how long it would take jerry working alone.

rate * time = quantity

quantity = 1
rate = 1/(6-3) = 1/3

your equation becomes:

1/3 * time = 1

solve for time to get time = 3 hours.

it would take jerry 3 hours to do the job working alone.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
Jerry can lay a tile floor in 3 hours less time than Jake. If they can work together, the floor takes 2 hours. How long would it take Jerry to lay the floor by himself?

Let time Jerry takes be J
Then Jerry can do of the floor in 1 hour
Also, time Jake takes = J + 3
Jake can do of floor in 1 hour
With them working together, we get:
2(J + 3) + 2J = J(J + 3) ------ Multiplying by LCD, 2J(J + 3)

(J - 3)(J + 2) = 0
J, or time it takes Jerry, alone = hours OR J = - 2(ignore)