SOLUTION: Can you please help me with this "filling storage tanks" word problem? Two pipes ure used to fill a water storage tank. The first pipe can fill the tank in 4hrs, and the two pipes

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Question 211575This question is from textbook
: Can you please help me with this "filling storage tanks" word problem? Two pipes ure used to fill a water storage tank. The first pipe can fill the tank in 4hrs, and the two pipes together can fill the tank in 2 hrs less time than the second pipe alone. How long would it take for the second pipe to fill the tank? please show me all the steps and please get back before Tues 10am.
Thanks guys This question is from textbook

Found 4 solutions by ankor@dixie-net.com, checkley77, Edwin McCravy, Theo:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two pipes are used to fill a water storage tank.
The first pipe can fill the tank in 4 hrs, and the two pipes together can fill
the tank in 2 hrs less time than the second pipe alone.
How long would it take for the second pipe to fill the tank
:
Let t = time for the 2nd pipe to fill it alone
then
(t-2) = two hrs less
:
Let the completed job (full tank) = 1
:
%28t-2%29%2F4 + %28t-2%29%2Ft = 1
Multiply equation by 4t, results:
t(t-2) + 4(t-2) = 4t
:
t^2 - 2t + 4t - 8 = 4t
:
Arrange as a quadratic equation:
t^2 - 2t + 4t - 4t - 8 = 0
:
t^2 - 2t - 8 = 0
Factor
(t-4)(t+2) = 0
Positive solution:
t = 4 hrs is 2nd pipe time alone
:
:
Check solution in original equation
%284-2%29%2F4 + %284-2%29%2F4 = 1
2%2F4 + 2%2F4 = 1

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
4X/(4+X)=(X-2)
4X=(4+X)(X-2)
4X=4X+X^2-2X-8
4X-4X=X^2-2X-8
X^2-2X-8=0
(X-4)(X+2)=0
X-4=0
X=4 HOURS FOR THE SECOND PIPE TO FILL THE TANK WORKING ALONE.
PROOF:
4*4/(4+4)=4-2
16/8=2
2=2

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please help me with this "filling storage tanks" word problem? Two pipes ure used to fill a water storage tank. The first pipe can fill the tank in 4hrs, and the two pipes together can fill the tank in 2 hrs less time than the second pipe alone. How long would it take for the second pipe to fill the tank? please show me all the steps and please get back before Tues 10am.

Make this chart
             
          # tanks filled   rate in tanks/hr   time in hrs  
1st pipe           
2nd pipe        
together         

Let's let t represent the number of hours for the second
pipe to fill 1 tank.  So we fill in 1 for the # of tanks
filled and t for the time in hours.

          tanks filled   rate in tanks/hr   time in hrs  
1st pipe      
2nd pipe       1                                 t
together

>>...The first pipe can fill the tank in 4hrs...<<

So that's 1 tank in 4 hours, so fill in 1 for the
tanks filled, and 4 for the time: 

         # tanks filled   rate in tanks/hr   time in hrs  
1st pipe       1                                 4
2nd pipe       1                                 t    
together

>>...the two pipes together can fill the tank in 2 hrs less time than the second pipe alone...<<

So together they fill exactly 1 tank in t-2 hours.  So
fill in 1 for the # tanks filled an t-2 for the number of hours


         # tanks filled   rate in tanks/hr   time in hrs  
1st pipe       1                                 4
2nd pipe       1                                 t
together       1                                t-2


To find the rates in tanks per hr, we divide the number
of tanks by the number of hours in each case:


         # tanks filled   rate in tanks/hr   time in hrs  
1st pipe       1              1/4                4
2nd pipe       1              1/t                t
together       1            1/(t-2)             t-2

The rate together is equal to the sum of the separate rates,
so

(Rate of 1st pipe) + (Rate of 2nd pipe) = (Rate together)

So the equation is 

            1%2F4%2B1%2Ft=1%2F%28t-2%29

Solve that and get two solutions

t=-2 and t=4

The negative solution is discarded and
the only solution is 4 hours for the 
second pipe to fill the tank.

Edwin

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
rate * time = number of gallons filled
-----
r1 = hose 1 rate
t1 = hose 1 time
r2 = hose 2 rate
t2 = hose 2 time
g = number of gallons
-----
r1*t1 = g
t1 = 4
4*t1 = g
t1 = g/4
-----
r2*t2 = g
r2 = g/t2
-----
(r1+r2)*(t2-2) = g
substitute g/4 for r1 and g/t2 for r2 to get:
(g/4 + g/t2) * (t2-2) = g
-----
divide both sides of equation by g to get:
(1/4 + 1/t2) * (t2-2) = 1
-----
multiply both sides of the equation by 4*t2 to get:
(t2 + 4) * (t2 - 2) = 4*t2
multiply factors out to get:
(t2)^2 + 4*t2 - 2*t2 - 8 = 4*t2
-----
subtract 4*t2 from both sides of the equation and combine like terms to get:
(t2)^2 - 2*t2 - 8 = 0
-----
factor this to get:
(t2 - 4) * (t2 + 2) = 0
-----
t2 = 4 OR t2 = -2
-----
since t2 can't be negative, only good solution would be:
t2 = 4
-----
Answer is it takes pipe 2 4 hours to fill the tank.
-----
let g be any number of gallons.
suppose 100 gallons
-----
4r1 = 100
r1 = 25
4r2 = 100
r2 = 25
working together we get:
(r1+r2)*2 = 100
(50)*2 = 100
100 = 100
-----
checks out ok.
hose 1 takes 4 hours
hose 2 takes 4 hours
working together they take 2 hours
-----