Answer:A and B together can complete the work in 1/3 of a day, which is approximately 0.33 days or 8 hours.So, A and B will finish the work alone in approximately 0.33 days or 8 hours.
Explanation:
A and B can do the work in 6 days:
Their combined work rate is a + b = 1/6.B and C can do the work in 10 days:
Their combined work rate is b + c = 1/10.C and A can do the work in 15 days:
Their combined work rate is c + a = 1/15.We need to find how many days it will take for A and B to finish the work when working together.To solve this, we can add the equations for A and B, and we get:
(a + b) + (b + c) + (c + a) = 1/6 + 1/10 + 1/15.Simplifying the equation gives us:
2a + 2b + 2c = 1/6 + 1/10 + 1/15.Combining the fractions on the right side gives us:
2a + 2b + 2c = (5 + 3 + 2) / 30.Simplifying the right side gives us:
2a + 2b + 2c = 10/30.Further simplifying, we have:
2(a + b + c) = 1/3.Since a + b is the combined work rate of A and B, we can write it as 1/3:
2(1/3) = 1/3.