Question

if A and B together can do a piece of work in 10 days and B along can do it in 15 days, how many part of the work does A complete in 6 days ​

Answer 1

1/5

Explanation:

Well work can be defined as:
`work = rate \ *\ time`

where rate=amount of work that can be done in one unit of time

let a = rate of work A does in a day

let b = rate of work B does in a day

this means that:
`10a + 10b=1` where work=1 and it just means the entire job has been completed.

Since b can do it alone in 15 days, this means that:
`15b=1`

If we divide by 15 here, we get the equation:
`b=(1)/(15)`

We can now use this definition to substitute it into the first equation we made.

`10a + 10((1)/(15)) = 1`

Multiply the 10 and 1/15

`10a+(2)/(3)=1`

subtract 2/3 from both sides

`10a=(1)/(3)`

Now divide both sides by 10

`a=(1)/(30)`

Now multiply this by 6, since we a represents the amount of work that can be done in a day, we want to find how many parts of the work can be done by a in 6 days

`6a=(6)/(30)`

Now divide both the numerator and denominator by 6

`a=(1)/(5)`