John can dig the garden in 30 minutes while Jack takes 20 minutes. How long should it take if they work together?

To solve this problem, we need to find out how much of the garden each person can dig in one minute, then add these amounts together to find out how much they can dig together in one minute.

1. John can dig the garden in 30 minutes, so in one minute, he can dig 1/30 of the garden.
2. Jack can dig the garden in 20 minutes, so in one minute, he can dig 1/20 of the garden.
3. If they work together, in one minute, they can dig 1/30 + 1/20 of the garden.

To add these fractions, we need to find a common denominator. The least common multiple of 30 and 20 is 60, so we convert the fractions to have this denominator:

1/30 = 2/60 1/20 = 3/60

So together, they can dig 2/60 + 3/60 = 5/60 of the garden in one minute.

4. To find out how long it would take them to dig the whole garden, we take the reciprocal of this fraction, which gives us 60/5 = 12 minutes.

So, it should take them 12 minutes to dig the garden if they work together.