How am I just learning this now?
Here is how hopeless I am with ratios and all that.
How to solve a COMBINED WORK PROBLEM
In a combined work problem, you are given the rate at which people are machines perform work individually and asked to compute the rate at which they work together (or vice versa). The work formula states: The inverse of the time it would take everyone working together equals the sum of the inverses of the times it would take each working individually. In other words:
1/r + 1/s = 1/t
where r and s are, for example, the number of hours it would take Rebecca and Sam, respectively, to complete a job working by themselves, and t is the number of hours it would take the two of them working together. Remember that all these variables must stand for units of TIME and must all refer to the amount of time it takes to do the same task.
Example:
If it takes Joe 4 hours to paint a room and Pete twice as long to paint the same room, how long would it take the two of them, working together, to paint the same room, if each of htem works at his respective individual rate?
Setup:
Joe takes 4 hours, so Pete takes 8 hours; thus:
1/4 + 1/8 = 1/t
2/8 + 1/8 = 1/t
3/8 = 1/t
t = 1/(3/8) = 8/3
So it would take them 8/3 hours, or 2 hrs 40 mins, to pain the room together.
Dude, this would have been so helpful much earlier! Like high school. How did I not know this formula beforehand?
How to solve a COMBINED WORK PROBLEM
In a combined work problem, you are given the rate at which people are machines perform work individually and asked to compute the rate at which they work together (or vice versa). The work formula states: The inverse of the time it would take everyone working together equals the sum of the inverses of the times it would take each working individually. In other words:
1/r + 1/s = 1/t
where r and s are, for example, the number of hours it would take Rebecca and Sam, respectively, to complete a job working by themselves, and t is the number of hours it would take the two of them working together. Remember that all these variables must stand for units of TIME and must all refer to the amount of time it takes to do the same task.
Example:
If it takes Joe 4 hours to paint a room and Pete twice as long to paint the same room, how long would it take the two of them, working together, to paint the same room, if each of htem works at his respective individual rate?
Setup:
Joe takes 4 hours, so Pete takes 8 hours; thus:
1/4 + 1/8 = 1/t
2/8 + 1/8 = 1/t
3/8 = 1/t
t = 1/(3/8) = 8/3
So it would take them 8/3 hours, or 2 hrs 40 mins, to pain the room together.
Dude, this would have been so helpful much earlier! Like high school. How did I not know this formula beforehand?