Question 207761: I have received the solution that you sent to me..thanks a lot. but i need again your help..ive been trying to solve this a lot of times but it seems that my knowledge is not yet enough...can you help me solve these two problems??
1)A water tank is supplied by pipes A and B and emptied by pipe C. If the pipes are open, the tank can be filled in 15 hours. If the tank is full and pipes A and C are open, the tank can be emptied in 10 hours. If the tank is full and pipes B and C are open, the tank can be emptied in 6 hours. If pipe A supplies 50 more liters a minute than pipe B and the capacity of the tank is 45 000 liters, find the number of liters that pass through each pipe per minute.
2)A contractor worked for 7 days after which he sought the help of his son and together they finished a painting job in 5 days. Had he sought the help of his son 3 days after he started working, they would have finished the job in 7 days. How long would it take each to finish the job alone?
Im hoping for an immediate response, thanks a lot.godbless
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 1)A water tank is supplied by pipes A and B and emptied by pipe C.
If the pipes are open, the tank can be filled in 15 hours.
If the tank is full and pipes A and C are open, the tank can be emptied in 10 hours.
If the tank is full and pipes B and C are open, the tank can be emptied in 6 hours.
If pipe A supplies 50 more liters a minute than pipe B and the capacity of the
tank is 45 000 liters, find the number of liters that pass through each pipe per minute.
Let A, B, C = the capacities of the three pipes (in liters per hour)
:
Write an equation for each statement:
:
"If the pipes are open, the tank can be filled in 15 hours.
Eq1: 15A + 15B - 15C = 45000 (full is plus)
:
"tank is full and pipes A and C are open, the tank can be emptied in 10 hrs."
Eq2: 10A - 10C = -45000 (emptied is minus)
:
"tank is full and pipes B and C are open, the tank can be emptied in 6 hrs"
Eq3: 6B - 6C = -45000
:
"pipe A supplies 50 more liters a minute than pipe B "
Eq4: A = B + 60(50)
A = B + 3000; converted to liters per hr
:
Using eq1 and 4, substitute (B+3000) for A
15(B+3000) + 15B - 15C = 45000
15B + 45000 + 15B - 15C = 45000
30B - 15C = 45000 - 45000
30B - 15C = 0
Therefore
30B = 15C
Simplify, divide by 2
2B = C
:
Using eq3:
6B - 6C = -45000
Simplify, divide by 6
B - C = -7500
substitute 2B for C
B - 2B = -7500
-B = -7500
B = 7500 liters/min, B pipe
Then
2B = C
therefore
2(7500) = C
C = 15000 liters/min, C pipe
:
Find A using eq4
A = B + 3000
A = 7500 + 3000
A = 10500 liters/min, A pipe
:
:
Check solutions in eq1, using a calc:
15(10500) + 15(7500) - 15(15000) = 45000
;
:
2)A contractor worked for 7 days after which he sought the help of his son and
together they finished a painting job in 5 days. Had he sought the help of his
son 3 days after he started working, they would have finished the job in 7 days.
How long would it take each to finish the job alone?
:
Let x = time for Dad alone
Let y = time for son alone
Let the completed job = 1
:
write an equation for each scenario.
:
1st scenario Dad works a total of 12 days
 +  = 1
Multiply by xy, results
12y + 5x = xy
:
2nd scenario Dad works a total of 10 days
 +  = 1
multiply by xy, results
10y + 7x = xy
:
Therefore
12y + 5x = 10y + 7x
12y - 10y = 7x - 5x
2y = 2x
y = x
:
This greatly simplifies things, using the first equation, replace y with x:
+  = 1
Multiply by x
12 + 5 = x
x = 17 days, Dad working alone
and
y = 17 days, son working alone
:
Checks out in the 2nd equation
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