Vahe and davit together can complete a task in 3 days. if they had to work separately, the time taken by davit to complete it would be more than that of vahe by 8 days. in how many days can vahe alone complete the task?

4 days

Step-by-step explanation:

When combining rates you are basically adding fractions.  so if we say Vahe can do v (as a variable) tasks per 3 days and Davit can complete d tasks per 3 days it would look like

now, we know that vahe can complete a task in let's say x days and Davit can complete the task in x+8 days so that means and .  If we can find x we can make these into the v and d terms above, so we need to find x.  If we add these two fractions, like we do the stuff above, we get = .  so now we can set =

from here it's algebra.

= Cross multiply

3(2x+8) = x(x+8) expand

6x + 24 = x^2 +8x Get everything to one side

0 = x^2 + 2x  -24 Factor however you like, I can go through it if you also want.

You wind up with  x = 4

So, now we can plug into the equation with x.  So vahe can complete a task in 4 days and Davit 12 days.  We can check by adding the fractions [tex]\frac{1}{4} + \frac{1}{12} which gives us that 1/3

false

step-by-step explanation: