Question 25656
Work done = (rate)(time)
Nancy rate is 1/(3/2)=(2/3)job/hr.
Let Sister's time to do the job be "x"; then her rate is 1/x.
Note that 40min.= 2/3 hr.
EQUATION:
Working together their rate is (2/3+1/x)job/hr.
Amount of time to do job together is 2/3 hr.
(2/3 + 1/x)(2/3) = 1
(2/3 + 1/x)= 3/2
(2x+3)/3x =3/2
4x+6=9x
 5x=6
  x=1 1/5 = 1hr + (1/5)hr. = 1 hr. + 12 min.

Cheers,
Stan H.