A and B can do a piece of work in 10 days B and C can do it in 15 days and a and c can do it in 20 days how long will they take to do it together and individually​

let's define:

a = rate at which A works

b = rate at which B works

c = rate at which C works.

We know that A and B can do a piece of work in 10 days, then we have the equation:

(a + b)*10 days = 1 piece of work

B and C can do it in 15 days, then we get:

(b + c)*15 days = 1 piece of work

A and C can do it in 20 days, then we get:

(a + c)*20 days = 1 piece of work

Then we could write it (in a simplified way) as:

(a + b)*10 = 1

(b + c)*15 = 1

(a + c)*20 = 1

remember that the units of each rate will be (piece of work/day)

Now, to solve the system, we need to start by isolating one of the variables in one of the equations, i will isolate a in the first equation.

(a + b)*10 = 1

(a + b) = 1/10

a = (1/10 - b)

Now we can replace this in the third equation, and now our system is:

(b + c)*15 = 1

(1/10 - b + c)*20 = 1

Now we need to isolate another variable, i will isolate b in the first equation.

(b + c)*15 = 1

(b + c) = 1/15

b = 1/15  - c

Now we can replace this in the other equation to get:

(1/10 - ( 1/15  - c) + c)*20 = 1

(1/10 - 1/15 + 2*c)*20 = 1

Let's solve this for c.

(1/10 - 1/15 + 2*c) = 1/20

2*c = 1/20 - 1/10 + 1/15 = 3/60 - 6/60 + 4/60 = 1/60

c = (1/60)/2 = 1/120

With this, we can find the value of b.

b = 1/15  - c = 1/15 - 1/120 = 8/120 - 1/120 = 7/120

And with this we can find the value of a.

a = 1/10 - 7/120 = 12/120 - 7/120 = 5/120

Then we have:

c = 1/120  pieces of work per day.

b = 7/120 pieces of work per day

a = 5/120 pieces of work per day.

Now, to find how much time each one of them needs to complete a piece of work we need to solve:

C)  (1/120 pieces of work per day)*T = 1 piece of work

T = (1 piece of work)/(1/120 pieces of work per day) = 120 days

C needs 120 days.

B)  (7/120 pieces of work per day)*T = 1 piece of work

T = (1 piece of work)/(7/120 pieces of work per day) = 17.1 days

B needs 17.1 days

A) (5/120 pieces of work per day)*T = 1 piece of work

T = (1 piece of work)/(5/120 pieces of work per day) = 24 days

A needs 24 days

And if the 3 work together, we have:

(a + b + c)*T = 1 piece of work

ignoring the units only for the calculation, we get:

(1/120 + 7/120 + 5/120)*T = 1

(13/120)*T = 1

T = 1/(13/120) = 9.23

The 3 working together need 9.23 days.

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: