Mike and Mindy can make paintings in 6 days, Mindy and Josh can make those paintings in 10 days. If Mike, Mindy & Josh together can finish the work in 4 days, then Mike & Josh together will do it in how many days?
Mike and Mindy’s 1 day work = 1/6
Mindy and Josh’s 1 day work = 1/10
Mike, Mindy and Josh’s 1 day work = 1/4
So, Mike and Josh’s 1 day work = 2 × (Mike, Mindy and Josh’s 1 day work) - (Mike and Mindy’s 1 day work) - (Mindy and Josh’s 1 day work)
⇒ 2 × (1/4) - (1/6) - (1/10)
⇒ (1/2) - (4/15) = 7/30
∴ Time taken by Mike and Josh to complete the painting = 1/(7/30) = 30/7 = $(4\frac{2}{7}{\rm{\;days}})$