SOLUTION: What ever shall I do to solve this problem? Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How

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Question 324678: What ever shall I do to solve this problem?
Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone?
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone?
----------------
2-pipes DATA:
time = 10 hr/job ; rate = 1/10 job/hr
-------------------------
1-pipe DATA:
time = 15 hr/job ; rate = 1/15 job/hr
-----
Other pipe DATA:
time = x hr/job ; rate = 1/x job/hr
---------------------------------------
Equation:
rate + rate = together rate
1/x + 1/15 = 1/10
---
Multiply thru by 30x to get:
30 + 2x = 3x
x = 30 hr. (time required by "Other" pipe)
========================
Cheers,
Stan H.
==================

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Output
Let Pipe 1's rate be R1, Let Pipe 2's rate be R2.
The output will be 1 to fill the large tank.
1.%28R1%2BR2%2910=1
2.R1%28t%2B10%29=1
3.R2%2At=1
From eq. 1,
R1%2BR2=1%2F10
From eq. 2,
t%2B15=1%2FR1
t=1%2FR1-15
From eq. 3,
R2%2At=1
t=1%2FR2
Equate the t equations,
1%2FR1-15=1%2FR2
1%2FR1-1%2FR2=15
4.R2-R1=15R1%2AR2
From above,
R1=%281%2F10%29-R2
Substitute into eq. 4,
R2-%28%281%2F10%29-R2%29=15%28%281%2F10%29-R2%29%29R2
R2-1%2F10%2BR2=15%28R2%2F10-R2%5E2%29
2R2-1%2F10=%283%2F2%29R2-15R2%5E2
40R2-2=30R2-300R2%5E2
300R2%5E2%2B10R2-2=0
You can factor this quadratic,
%2830R2-2%29%2810R%2B1%29=0
Only a positive rate makes sense in this case.
30R2-2=0
30R2=2
R2=2%2F30
highlight_green%28R2=1%2F15%29
Then from eq. 1,
R1%2BR2=1%2F10
R1%2B1%2F15=1%2F10
R1=3%2F30-2%2F30
highlight_green%28R1=1%2F30%29
.
.
.
R1%2At1=1
t1=1%2FR1
highlight%28t1=30%29hrs
.
.
.
R2%2At2=1
t2=1%2FR2
highlight%28t2=15%29 hrs