SOLUTION: Please help me solve these problems. I did them but the answer I'm getting seems way off. Apply algebraic techniques to solve rate problems and percent problems: 4,) A painte

Question 151482: Please help me solve these problems. I did them but the answer I'm getting seems way off.
Apply algebraic techniques to solve rate problems and percent problems:
4,) A painter can do a given job in 6 hours. Her helper can do the same job in 10 hours. The painter begins the work and after two hours is joined by the helper. In how many hours will they complete the job?
5.) One group of workers can do a job in 8 days. After this group has worked 3 days, another group joins it and together they complete the job in 3 more days. In what time could the second group complete the job alone?
6.)What weight of water must be evaporated from 40lb of a 20% of salt solution to produce 50% solution? All percentages are by weight.
Thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Apply algebraic techniques to solve rate problems and percent problems:
4,) A painter can do a given job in 6 hours. His helper can do the same job in 10 hours. The painter begins the work and after two hours is joined by the helper. In how many hours will they complete the job?
:
Let t = no. of hrs required for them to complete the job
Let the completed job = 1
:
Painter will be on the job = (t+2)
Helper will be on the job = t
:
We want to determine what fraction of the job is done by each (has to add up to 1)
+ = 1
Multiply equation by 30
30* + 30* = 30(1)
Cancel out the denominators and you have:
5(t+2) + 3t = 30
:
5t + 10 + 3t = = 30
:
8t = 30 - 10
t =
t = 2.5 hrs with the helper on the job
:
:
Check solution on calc
+ =
.75 + .25 = 1
:
;
5.) One group of workers can do a job in 8 days. After this group has worked 3 days, another group joins it and together they complete the job in 3 more days. In what time could the second group complete the job alone?
:
Let x = time required by group 2 to complete the job
Let the completed job = 1
:
Group 1 works a total of 6 days
Group 2 works a total of 3 days
:
+ = 1
Multiply equation by 8x to get rid of the denominator, results:
6x + 3(8) = 8x
:
24 = 8x - 6x
:
24 = 2x
x =
x = 12 days, for group 2
:
Check solution on calc
(6/8) + (3/12) = 1
:
:
6.)What weight of water must be evaporated from 40lb of a 20% of salt solution to produce 50% solution? All percentages are by weight.
:
Let amt of water to evaporated = x
:
write amt of salt equation
.20(40) = .50(40-x)
8 = 20 - .5x
8 - 20 = -.5x
-12 = -.5x
x =
x = +24 lb to be evaporated
:
Check solution:
.2(40) = .5(40-24)
8 = .5(16)

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