three men A B C working together can do a job in 6 hrs less time than A alone, in 1 hr less time than B alone and in one half the time needed by C when working alone. then A and B together can do a job in.
Let x = the number of hours it takes A to do 1 job working alone.
Let y = the number of hours it takes B to do 1 job working alone.
Let z = the number of hours it takes C to do 1 job working alone.
Let t = the number of hours it takes A,B, and C to do 1 job working together.
Then
three men A B C working together can do a job in 6 hrs less time than A alone,
t = x - 6
(1) x = t + 6
in 1 hr less time than B alone
t = y - 1
(2) y = t + 1
and in one half the time needed by C when working alone.
t =
2t = z
(3) z = 2t
A's working rate =
B's working rate =
C's working rate =
The combined working rate of all three working together =
(4)
Substituting from (1), (2), and (3) into (4)
Multiply through by the LCD, and get t = hour, after dicarding
the negative value for t.
Substituting in (1), (2), and (3) we get that
A can do 1 job in 20/3 hours.
B can do 1 job in 5/3 hours.
C can do 1 job in 4/3 hours.
But that's not what we are asked to find. What we are asked to find is
given by this sentence:
A and B together can do a job in ____ hours.
A's working rate =
B's working rate =
Suppose it takes them h hours to complete the job. Then
The combined working rate of A&B working together =
Multiply through by an LCD, solve and get h = 4/3 hr or 1 hour and 20 minutes.
Edwin