Work problems ask you to find out how much work gets done in a certain amount of time. You use this formula for doing algebra work problems:
Production = Rate of Work × Time
Production means the amount of work that gets The production is the product of the rate times the time.
The amount of work (W) accomplished in time (T) depends on the rate (R) at which the work is being done. Thus, W = RT. Assuming work to be constant, rate of doing work and time are inverse. For example, faster the speed at which you complete your work, lesser will be the time required.
Majority of the GMAT problems involve two persons or two machines. The rates at which certain persons or machines work alone are usually given, and it is required to compute the rate at which they work together (or vice versa).
Rate = Work / Time
Suppose a person A works for N days, then he can do 1/N of the work in 1 day.
Similarly, suppose another person B works for M days, then he can do 1/M of the work in 1 day.
(Rate of A alone) + (Rate of B alone) = (Combined rate of A & B)
Now, if both A and B work together, then they can do (1/N + 1/M) work in 1 day. If H is time (or hours) required by both of them doing work together, then:
1/M + 1/N = 1/H
Example 1: If Machine X can produce 1,000 bolts in 4 hours and Machine Y can produce 1,000 bolts in 5 hours, in how many hours can Machines X and Y, working together at these constant rates, produce 1,000 bolts?
1/4 + 1/5 = 1/h
h = 20/9
Working together, Machines X and Y can produce 1,000 bolts in 20/9 hours.
Example 2: If Arti and Rita can do a job in 4 hours when working together at their respective constant rates and Arti can do the job alone in 6 hours, in how many hours can Rita do the job alone?
1/6 + 1/R = 1/4
R = 12
Working alone, Rita can do the job in 12 hours.