The ratio of the number of days it takes the first team to complete the project to the number of days it takes the second team to complete the project is 2:3. If together the two teams can finish the work in 6 days, how many days does it take each team to complete the project on their own?

Time taken by first team by their own = 10 days

Time taken by second team by their own = 15 days

Step-by-step explanation:

Given that:-

The ratio of the number of days taken by the first team to that of second team = 2:3

Let the number of days taken by first team = 2x days

Let the number of days taken by second team = 3x days

Let the work to be done = 6x units

So, Efficiency of first team = 6x units / 2x days = 3 units/day

Efficiency of second team = 6x units / 3x days = 2 units/day

If they work together they complete in 6 days, then total efficiency = 5 units/day

So,

5 units / day * 6 days = 6x units

x = 5 units

Total work = 30 units

Time taken by first team by their own = 30 units / 3 units/day = 10 days

Time taken by second team by their own = 30 units / 2 units/day = 15 days