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.

step-by-step :

i would be 2,000 just get the square root of 50 which is 2500 and the divid 4/5 and last thing multiply the answer you get for that by the square root of 50

step-by-step explanation: