Let's analyze the problem step-by-step.
Problem Restatement:
- Worker A can finish the job in 20 days.
- Worker B can finish the job in 30 days.
- They start working together.
- Worker B leaves x days before the job is completed.
- We need to find the total number of days T it takes to finish the job.
Step 1: Define variables and rates
- Let the total time to complete the job be TTT days.
- B leaves xxx days before completion, so B works for T−xT-xT−x days.
- A works for the full TTT days.
Work rates:
- A's rate = 120\frac{1}{20}201 of the job per day.
- B's rate = 130\frac{1}{30}301 of the job per day.
Step 2: Write the work done equation
Total work done = 1 (whole job) Work done by A = 120×T\frac{1}{20}\times T201×T Work done by B = 130×(T−x)\frac{1}{30}\times (T-x)301×(T−x) Sum of work done by A and B:
T20+T−x30=1\frac{T}{20}+\frac{T-x}{30}=120T+30T−x=1
Step 3: Simplify the equation
Multiply both sides by 60 (LCM of 20 and 30):
3T+2(T−x)=603T+2(T-x)=603T+2(T−x)=60
3T+2T−2x=603T+2T-2x=603T+2T−2x=60
5T−2x=605T-2x=605T−2x=60
Step 4: Additional information needed
The problem as stated is incomplete because it does not specify how many days before completion B leaves (value of xxx) or any other condition to relate TTT and xxx.
Conclusion:
To find the exact number of days TTT, the problem needs one more piece of information, such as:
- The value of xxx (how many days before completion B leaves), or
- The total time TTT is given or related to xxx,
- Or the amount of work done by A alone after B leaves.
If you provide the number of days B leaves before completion or any additional detail, I can help solve for TTT.
