time and work

Question

two pipes a and b can fill a tank in 6 hours and 8 hours .if both pipes are opened together ,then after how many hours B should be closed ,so that the tank is full in 4 hours.

 

(a)5

(b)4/3

(c)2

(d)8/3

Answer 1

This problem involves a joint rate.   A key to joint rate problems is that rates add.

 

The rate   for  pipe a  ,  R_a ,    is  R_a  =  1/6     (unit is tanks per hour)

 The rate for pipe b,   R_b  ,     is   R_b  = 1/8       (unit is tanks per hour)

 

  The joint rate, R_J ,   is thus   R_J   =1/6 + 1/8  =  7/24        (tanks per hour)

 

 Let the number of hours for which both pipes run be x ,  and consequently, the number of hours for which only pipe a runs will be    4 -x

 

    The condition that the tank be filled in 4 hours is then:

    1 =  R_J  x  +  R_a  (4-x)

 

    1 =  (7/24) x  + (1/6) (4-x)

 

   Solving for x  gives  x =  8/3