Question

If m workers can complete a job in d days, how many days will it take n workers, working at the same rate, to complete one third of the job? Express your answer as a common fraction in terms of d, m and n

Answer 1

`Time=(md)/(3n)`

Explanation:

We can use the formula shown below to solve this problem.

RWT = J

Where

R is the rate

W is the workers

T is the time

J is the number of jobs

First,

W = m

T = d

J = 1 [since it is said 1 job]

Lets find the Rate (R):

RWT = J

R(m)(d) = 1

R =
`(1)/(md)`

Now, using this value of R, we are going to find T, given:

W = n

J = 1/3

R = 1/md (found earlier)

So, let's find T:

RWT = J

`((1)/(md))(n)T = (1)/(3)\\((n)/(md))T=(1)/(3)\\T=((1)/(3))/((n)/(md))\\T=(1)/(3)*(md)/(n)\\T=(md)/(3n)`

This is the time it will take, in terms of d, m, and n