SOLUTION: A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T       Log On


   

Question 685827: A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T + 45 days. What is T?
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T + 45 days. What is T?
Their combined rate is 1 job per T days or %281_job%29%2F%28T_days%29 or 1%2FTjob%2Fday

A's rate is 1 job per T+5 days or %281_job%29%2F%28T%2B5_days%29 or 1%2F%28T%2B5%29job%2Fday

B's rate is 1 job per T+45 hours or %281_job%29%2F%28T%2B45_days%29 or 1%2F%28T%2B45%29job%2Fdays

The equation comes from %28matrix%284%2C1%2C%0D%0A%0D%0A%22A%27s%22%2C+rate%2C+in%2C+%22job%2Fdays%22%29%29 + %28matrix%284%2C1%2C%0D%0A%0D%0A%22B%27s%22%2C+rate%2C+in%2C+%22job%2Fdays%22%29%29 = %28matrix%285%2C1%2C%0D%0A%0D%0ATheir%2C+combined%2C+rate%2C+in%2C+%22job%2Fdays%22%29%29

                                     1%2F%28T%2B5%29 + 1%2F%28T%2B45%29 = 1%2FT

Multiply through by LCD = T(T+5)(T+45) and solve.  You'll get T = 15 days.

Edwin

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A's rate working alone is +1%2F%28+T+%2B+5+%29+
B's rate working alone is +1%2F%28+T+%2B+45+%29+
Working together:
+1%2F%28+T%2B5+%29+%2B+1%2F%28+T%2B45+%29+=+1%2FT+
Multiply both sides by +T%2A%28+T%2B5+%29%2A%28+T+%2B+45+%29+
+T%2A%28+T+%2B+45+%29+%2B+T%2A%28+T+%2B+5+%29+=+%28+T%2B5+%29%2A%28+T%2B45+%29+
+T%5E2+%2B+45T+%2B+T%5E2+%2B+5T+=+T%5E2+%2B+5T+%2B+45T+%2B+225+
+T%5E2+=+225+
+T+=+15+