SOLUTION: Can you please help me with this? A software development company is getting ready to release a new product. The QA Director is notified the following. A Junior Verification Engine

Question 31561: Can you please help me with this?
A software development company is getting ready to release a new product. The QA Director is notified the following. A Junior Verification Engineer takes 1 hour longer to fix a bug (in the code) than it takes a Senior Engineer. If they can fix the bug in 5 hours working together, how long would it take each Engineer to finish the task by themselves?
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
Let the time taken by the Senior Engineer to fix the bug is x hrs
Time taken by the Junior Verification Engineer to fix the bug is (x+1) hrs
If the Sr. Engineer completes the full job in x hrs, he/she completes 1/x-th of the job in 1 hour.
=> Sr. Engineer completes 5/x portion of the job in 5 hours
Same way the Junior Verification Engineer completes 1/(x+1) portion of the job in 1 hour
=>Junior Verification Engineer completes 5/(x+1) portion of the job in 5 hours
Together they complete the entire job in 5 hours
=>5/x + 5/(x+1) = 1
=>5(x+1) + 5x = x(x+1)
=>10x+5 = x^2+x
=>x^2-9x-5 = 0
=>x=1/2[9+sqrt(81+20)] because number of hours cannot be negative
=>x=1/2[9+sqrt(101)]
=>x=1/2(9+10.05)
=>x=9.53
The Senior Engineer can fix the job in about 9:30 minutes individually and the Jr. Engineer can do the same in about 10:30 hours individually
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