SOLUTION: Please help me solve the following problem. Welder A works 3 times faster than welder B. Together they can do a job in 3 hours. How fast can the faster welder do the job by hims

Question 30924: Please help me solve the following problem. Welder A works 3 times faster than welder B. Together they can do a job in 3 hours. How fast can the faster welder do the job by himself? Thank you very much for helping me to solve this problem.
Found 2 solutions by acerX, mbarugel:
Answer by acerX(62) (Show Source): You can put this solution on YOUR website!
Welder A -> 3x
Welder B -> x
Total Time -> 3 hours
The equation would be:

Welder A -> 3x

or 2.25hours
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
Hello!
The previous answer you got for this question is actually incorrect.
This kind of problems can be solved in the following way. Let's call X to the rate at which welder A does the job per hour. For example, if he could complete the job in 10 hours, then this rate would be 1/10. He completes one tenths of the job per hour. Let's call Y to the same rate for Welder B.
We know that A's rate is 3 times higher than B's:

We also know thta if they work together, they complete the work in 3 hours. The rate at which they work together is X + Y. If they complete it in 3 hours, then the rate should be 1/3: they complete one third of the job per hour. So we have:

Replacing the 1st equation in the last one:

So Welder B by himself can complete the job in 12 hours. Since A is 3 times faster, he can complete the job by himself in 4 hours.

I hope this helps!
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