SOLUTION: Working together, Mr. Kent and Mr. Wayne can complete a job in 5 hours. If Mr. Wayne takes twice as long as Mr. Kent if each does the job alone, how long does it take Mr. Kent to

Question 1103341: Working together, Mr. Kent and Mr. Wayne can complete a job in 5 hours. If Mr. Wayne takes twice as long as Mr. Kent if each does the job alone, how long does it take Mr. Kent to complete the job alone?

Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = quantity of wrok performed is the equation that you can use to solve this.

let k be the rate that mr. kent works at.
let w be the rate that mr. wayne works at.
let 1 represent the quantity of work performed which is 1 job.
let T represent the time it takes.

your equation becomes:

(k + w) * T = 1

since T = 5, the equation becomes (k + w) * 5 = 1

you are given that mr. kent takes twice as long as mr. wayne to do the job alone.

this means that mr. wayne must be working twice as fast as mr. kent.

the rate for mr. wayne is 2 times the rate for mr. kent.

therefore, you get w = 2k.

your original formula of (k + w) * 5 = 1 becomes (k + 2k) * 5 = 1 after you replace w with 2k.

the formula becomes 3k * 5 = 1

solve for k to get k = 1/15.

since w = 2k, then w = 2/15.

mr. kent can complete 1/15 of the job in 1 hour.
mr. wayne can complete 2/15 of the job in 1 hour.

their combined rate is (k + w) = 1/15 + 2/15) = 3/15 of the job in 1 hour.

you get 3/15 * 5 = 1 which results in 1 = 1 which confirms the calculated rates for mr. kent and mr. wayne are correct.

when he is working alone, the formula for mr. kent becomes 1/15 * T = 1.
solve for T to get T = 15.
it would take mr. kent 15 hours to complete the job alone.

when he is working alone, the formula for mr. wayns becomes 2/15 * T = 1.
solve for T to get T = 7.5.
it would take mr kent 7.5 hours to complete the job alone.
that's twice as fast as it would take mr. kent working alone.

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1/k+1/w=1/x
k=w*0.5
1/w*0.5+1/w=1/5
1/w*0.5+0.5/0.5*w=1/5
1.5/w*0.5=1/5
0.5*w=7.5
w=15.0
k=15*0.5
k=7.5 w=15
check
1/k+1/w=1/x
1/7.5+1/15=1/5
0.13333333+0.66666667e-1=1/5
0.2=1/5
0.2=0.2
x=5 hours working together
k=7.5 hours working alone
w=15 hours working alone
ok
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