Question

A takes 6 hours more than (a + b +


c.Together to complete a work. B takes 1 hours more than (a + b + c)together to complete a work. C takes twice as (a +b+c) in how much time a+b wil complete the work

Answer 1

Answer:

4/3  hrs

Step-by-step explanation:

Let say a + b + c complete work  in  h Hours

=>  a + b + c   1 hr  work = 1/h

A takes 6 hours more than (a + b + c) = h + 6  hrs

=> a's 1 hr work  = 1/(h + 6)

B takes 1 hours more than (a + b + c) = h + 1

=> b's 1 hr work  = 1/(h + 1)

C takes twice as (a +b+c) = 2h

=> c's 1 hr work  = 1/2h

1/(h + 6) +  1/(h + 1) + 1/2h = 1/h

=> 1/(h + 6) +  1/(h + 1) = 1/2h

=> 2h(h + 1)  + 2h(h + 6)  = (h + 6)(h + 1)

=>  2h ( 2h + 7) = h² + 7h + 6

=> 4h² + 14h = h² + 7h + 6

=> 3h² + 7h - 6 = 0

=> 3h² + 9h - 2h - 6 = 0

=> 3h(h + 3) - 2(h + 3) = 0

=> h = 2/3

a + b 's   1 hr  Work  = a + b + c 's 1 hr work - c 's 1 hr  work

=> a + b 's   1 hr  Work  = 1/h - 1/2h  =  1/2h

a + b will complete work in 2h   = 2 * 2/3 = 4/3  hrs