SOLUTION: Good afternoon ma'am or sir. Will you please help me in solving this worded problems: 1). Ryoma can painttheir house 7 1/2 days, however Sakuno helped him and together they were a

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Good afternoon ma'am or sir. Will you please help me in solving this worded problems: 1). Ryoma can painttheir house 7 1/2 days, however Sakuno helped him and together they were a      Log On


   

Question 116938: Good afternoon ma'am or sir. Will you please help me in solving this worded problems:
1). Ryoma can painttheir house 7 1/2 days, however Sakuno helped him and together they were able to do the painting in just 4 days. If Sakuno work alone how many days would it take to paint the whole house?
2).A pipe can fill the pool in 6 hours. A small pipe can fill the pool in 8 hours. The pool will be empty within 12 hours. How long would it take to fill the pool if both filling pipe and draining pipe are both open?
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1). Ryoma can paint their house 7 1/2 days, however Sakuno helped him and together they were able to do the painting in just 4 days. If Sakuno work alone how many days would it take to paint the whole house?
:
Let x = S's time alone
Let the completed job = 1
:
Each will do a fraction of the house:
:
R's fraction + S's fraction = completed job
4%2F7.5 + 4%2Fx = 1
:
Multiply equation by 7.5x to get rid of the denominators:
7.5x*4%2F7.5 + 7.5x*4%2Fx = 7.5x(1)
Cancel out the denominators and you have;
4x + 7.5(4) = 7.5x
4x + 30 = 7.5x
30 = 7.5x - 4x
30 = 3.5x
x = 30/3.5
x = 8.57 days together or 8 days, 13.7 hrs
:
:
2).A pipe can fill the pool in 6 hours. A small pipe can fill the pool in 8 hours. The pool will be empty within 12 hours. How long would it take to fill the pool if both filling pipe and draining pipe are both open?
:
Let x = time required when working together
Let the full pool = 1
:
Let filling be positive & draining be negative:
x%2F6 + x%2F8 - x%2F12 = 1
:
Multiply equation by 24 to get rid of the denominators
24*x%2F6 + 24x%2F8 - 24x%2F12 = 24(1)
cancel out the denominators and you have:
4x + 3x - 2x = 24
:
5x = 24
:
x = 24/5
:
x = 4.8 hr to fill the pool (or 4 hrs 48 min)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1). Ryoma can paint their house 7 1/2 days, however Sakuno helped him and together they were able to do the painting in just 4 days. If Sakuno worked alone how many days would it take to paint the whole house?
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Ryoma DATA:
Time = (15/2) days/job ; Rate = (2/15) job/day
------
Together DATA:
Time = 4 days/job ; Rate = (1/4) job/day
--------
Sakuno DATA:
Time = x days/job ; Rate = 1/x job/day
-----------------
EQUATION:
rate + rate = together rate
2/15 + 1/x = 1/4
8x + 60 = 15x
7x = 60
x = 60/7 days = 8 4/7 days (Time for Sakuno to do the job alone.)
-------------------------

2).A pipe can fill the pool in 6 hours. A small pipe can fill the pool in 8 hours. The pool will be empty within 12 hours. How long would it take to fill the pool if both filling pipe and draining pipe are both open?
---------
1st Pipe DATA:
Time = 6 hrs/job ; Rate = 1/6 job/hr
2nd Pipe DATA:
Time = 8 hrs/job ; Rate = 1/8 job/hr
-----------------
Comment: You did not indicate which pipe is the draining pipe.
I will assume it is the 2nd Pipe because it works at a slower
rate; that would allow the filling pipe to actually fill the
pool.
--------------------
Together DATA:
Time = 12 hrs/job ; Rate = 1/12 job/hr.
-----------------
EQUATION:
Assume it takes x hrs to fill the tank when both filling and
emptying are takiing place.
x(1/6 - 1/8) = 1 job
x(2/48) = 1 job
x = 24 hrs
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Cheers,
Stan H.