SOLUTION: PLS ANYONE ANSWER THE FF.. 1.)Euclid works 2 times as fast as his siter.Together they cleaned the house in 4 hours.How long would it take each of them to clean the house? 2.)A sm

Algebra ->  Expressions -> SOLUTION: PLS ANYONE ANSWER THE FF.. 1.)Euclid works 2 times as fast as his siter.Together they cleaned the house in 4 hours.How long would it take each of them to clean the house? 2.)A sm      Log On


   

Question 519214: PLS ANYONE ANSWER THE FF..
1.)Euclid works 2 times as fast as his siter.Together they cleaned the house in 4 hours.How long would it take each of them to clean the house?
2.)A small pipe and a large pipe both carry water to storage tank.The large pipe fills the tank twice as fast as the small pipe.When both pipes are used,the tank is filled in 8 hrs.How long would it take the small pipe to fill the tank by itself?
3.)Working alone a man can mow a lawn in 3hours.His friend can complete the same job in 2hours.How long would it take them working together?
4.)A rope that is 20 feet long is cut into 2 pieces.The ratio of the smaller piece to the larger piece is 3/5.Find the length of the shorter piece.
5.)If 561 is divided by a certain number,the quotient is 29 and the remainder is 10.Find the number.
.need help..PLEASE!!!!!!!!!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The first three problems are all "shared work" problems and can be done in the same way.
I will complete the 1st one, and give the equation for the other two for you to do yourself.
:
:
1.)Euclid works 2 times as fast as his sitter.
Together they cleaned the house in 4 hours.
How long would it take each of them to clean the house?
:
let t = time for E to do the job
then
2t = time for his sitter to do the job
let the completed job = 1
4%2Ft + 4%2F%282t%29 = 1
multiply by 2t to get rid of the denominators
2t*4%2Ft + 2t*4%2F%282t%29 = 2t(1)
cancel the denominators, resulting in:
2(4) + 4 = 2t
8 + 4 = 2t
12 = 2t
t = 12/2
t = 6 hrs for E to do the job alone
then
2(6) = 12 hrs for his sitter to do it
:
Check these solutions ensuring that the two fractions add up to 1
4%2F6 + 4%2F12 =
4%2F6 + 2%2F6 = 1
:
:
2.)A small pipe and a large pipe both carry water to storage tank.
The large pipe fills the tank twice as fast as the small pipe.
When both pipes are used, the tank is filled in 8 hrs.
:
let t = time for the large pipe to fill the tank
then
2t = time required by the smaller pipe
let the completed job = 1 (full tank)
8%2Ft + 8%2F%282t%29 = 1
:
:
3.)Working alone a man can mow a lawn in 3hours.
His friend can complete the same job in 2hours.
How long would it take them working together?
;
let t = time required when working together
t%2F3 + t%2F2 = 1
:
:
4.)A rope that is 20 feet long is cut into 2 pieces.The ratio of the smaller piece to the larger piece is 3/5.
Find the length of the shorter piece.
:
let x = the multiplier
3x + 5x = 20
8x = 20
x = 20%2F8
x = 2.5 is the multiplier
the shorter rope (3x); 3*2.5 = 7.5 ft
:
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5.)If 561 is divided by a certain number,the quotient is 29 and the remainder is 10.
Find the number.
:
Let n = "that certain number"
561%2Fn = 29 + 10%2Fn
multiply thru by n, results:
561 = 29n + 10
561 - 10 = 29n
551 = 29n
n = 551%2F29
n = 19 is the number
:
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Let me know how you do on these. C