SivaKumarP wrote:
MBAhereIcome wrote:
this is a great post but, i'd suggest to use either of the below formulas depending on what the question asks.
time taken = A*B/A+B ............. where A,B is the respective time of each person/machine.
work done = W1 + W2 ............... where W1,W2 is the respective work done by each person/machine.
Can anyone help me how to use this formula for work problems?
Hi
SivaKumarP,
The formula is an extension of the basic concept of work rate problem. Let me explain it with an example.
Assume two persons A & B working alone who complete a work \('W'\) in \(5\) and \(6\) days respectively. We need to find the time taken by A & B working together to complete the same work \(W\).
We know the amount of work to be done (i.e. \(W\)) and are asked to find the time taken. From the work rate equation
Work = Rate * Time, the only variable remaining is the rate, so let's find out the rates of persons A & B and put in the equation to calculate the time taken.
Rates of work done by A & BWork done by A = \(W\)
Time taken by A to do W amount of work = \(5\) days
Since Rate = Work/time
Hence rate of work done by A = \(\frac{W}{5}\)Similarly rate of work done by B = \(\frac{W}{6}\)Putting the values of rates of A & B in the Work Rate equation to find out the time taken when both A & B work together:
Work = Rate * Time
\(W = (\frac{W}{5} + \frac{W}{6}) * t\)
(since A & B would work for the same time 't' to complete the work when working together)\(W = \frac{11W}{30} * t\) i.e. \(t = \frac{30}{11}\) days = \(\frac{(5*6)}{(5+6)}\) days
Time taken when A & B work together to do the same work = Time taken by A * Time taken by B/(Time taken by A + Time taken by B)On similar lines, if we need to find the work done by A & B working together for 30 days, we can calculate it using the rate of work of A & B working together which is \(\frac{11W}{30}\).
Work done by A & B working together for 30 days = \(\frac{11W}{30} * 30 = 11W = 6W + 5W\) i.e. work done by A & B respectively working alone for 30 days.
Work done by A & B together in time t = Work done by A in time t + Work done by B in time tHope its clear!
Regards
Harsh