A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in.40

Sure, let's solve this step by step.

1. First, we need to find out how long it would take for A and B to complete the work individually.

   A can do half of the work in 70 days, so A would take 70 * 2 = 140 days to complete the whole work.

   B can do one third of the work in 35 days, so B would take 35 * 3 = 105 days to complete the whole work.

2. Next, we need to find out how much work A and B can do in one day.

   A can do 1/140 of the work in one day, and B can do 1/105 of the work in one day.

3. If they work together, in one day they can do 1/140 + 1/105 of the work.

   To simplify this, we need to find a common denominator. The least common multiple of 140 and 105 is 420. So, we convert the fractions to have this common denominator:

   A can do 3/420 of the work in one day, and B can do 4/420 of the work in one day.

   Therefore, together they can do 3/420 + 4/420 = 7/420 of the work in one day.

4. To find out how long it would take for them to complete the whole work together, we divide the whole work (1) by the amount of work they can do together in one day (7/420).

   So, it would take them 1 / (7/420) = 420/7 = 60 days to complete the whole work together.