Found 3 solutions by Edwin McCravy, AnlytcPhil, Edwin Parker:
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A and B can do a piece of work in 42 days, B and C in 31 days and C and A in 20 days. In how many days can all of them do the work together?
A and B can do a piece of work in 42 days,
So A's and B's combined rate is 1 job per 42 days or or
B and C in 31 days
So B's and C's combined rate is 1 job per 31 days or or
C and A in 20 days
So C's and A's combined rate is 1 job per 31 days or or
Suppose A's rate working alone is is 1 job per x days or or .
Suppose B's rate working alone is is 1 job per y days or or .
Suppose C's rate working alone is is 1 job per z days or or .
Suppose their combined rate is 1 job per d days or or .
The four equations come from:
+ =
+ =
+ =
+ =
+ =
+ =
+ + =
+ + =
+ =
+ =
+ =
+ + =
Now we must find their combined rate which is
So we line up the first three equations like this and add them all:
+ =
+ =
+ =
---------------------
+ + =
+ + =
Dividing both side by 2
+ + =
And since the fourth equation is
+ + =
Since things equal to the same thing are equal to each other,
=
Cross-multiplying:
1381d = 26040
d =
d = 18.85590152 days
Edwin
Answer by AnlytcPhil(1807) (Show Source): You can put this solution on YOUR website!
A and B can do a piece of work in 42 days, B and C in 31 days and C and A in 20 days. In how many days can all of them do the work together?
A and B can do a piece of work in 42 days,
So A's and B's combined rate is 1 job per 42 days or or
B and C in 31 days
So B's and C's combined rate is 1 job per 31 days or or
C and A in 20 days
So C's and A's combined rate is 1 job per 31 days or or
Suppose A's rate working alone is is 1 job per x days or or .
Suppose B's rate working alone is is 1 job per y days or or .
Suppose C's rate working alone is is 1 job per z days or or .
Suppose their combined rate is 1 job per d days or or .
We wish to find d.
The four equations come from:
+ =
+ =
+ =
+ =
+ =
+ =
+ + =
+ + =
+ =
+ =
+ =
+ + =
So we line up the first three equations like this and add them all:
+ =
+ =
+ =
---------------------
+ + =
+ + =
Dividing both side by 2
+ + =
And since the fourth equation is
+ + =
Since things equal to the same thing are equal to each other,
=
Cross-multiplying:
1381d = 26040
d =
d = 18.85590152 days
Edwin
Answer by Edwin Parker(36) (Show Source): You can put this solution on YOUR website!
A and B can do a piece of work in 42 days, B and C in 31 days and C and A in 20 days. In how many days can all of them do the work together?
A and B can do a piece of work in 42 days,
So A's and B's combined rate is 1 job per 42 days or or
B and C in 31 days
So B's and C's combined rate is 1 job per 31 days or or
C and A in 20 days
So C's and A's combined rate is 1 job per 31 days or or
Suppose A's rate working alone is is 1 job per x days or or .
Suppose B's rate working alone is is 1 job per y days or or .
Suppose C's rate working alone is is 1 job per z days or or .
Suppose their combined rate is 1 job per d days or or .
The four equations come from:
+ =
+ =
+ =
+ =
+ =
+ =
+ + =
+ + =
+ =
+ =
+ =
+ + =
Now we must find their combined rate which is
So we line up the first three equations like this and add them all:
+ =
+ =
+ =
---------------------
+ + =
+ + =
Dividing both side by 2
+ + =
And since the fourth equation is
+ + =
Since things equal to the same thing are equal to each other,
=
Cross-multiplying:
1381d = 26040
d =
d = 18.85590152 days
Edwin
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