General formula for combined work rate
Last updated: 3 Jan 2009
The formula for solving combined work rate problems is
This general formula can be extended if more than 2 people (or machines are working together
Where , and are the times taken by A, B and C respectively to complete the task alone and is the time taken by them to complete the task when they are all working together.
We can use this formula to solve the same problem we faced on the previous page
If Alex can build a house in 2 days and his apprentice Bob can build a house in 3 days, then how long will it take Alex and Bob to build a house when they are working together?
Putting the information from the question into the formula gives us
Invert both sides of the equation
So Alex and Bob will take days to build a house when they are working together.