SOLUTION: A and B working together can do a job in 6 2/3 hours. A became ill after 3 hours of working with B. B finished the job, continuing to work alone, in 8 1/4 more hours. How long woul

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A and B working together can do a job in 6 2/3 hours. A became ill after 3 hours of working with B. B finished the job, continuing to work alone, in 8 1/4 more hours. How long woul      Log On


   



Question 507802: A and B working together can do a job in 6 2/3 hours. A became ill after 3 hours of working with B. B finished the job, continuing to work alone, in 8 1/4 more hours. How long would it take each working alone to do the job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = A's rate of working
Let +b+ = B's rate of working
given:
+a+%2B+b+=+1%2F%2820%2F3%29+
+a+%2B+b+=+3%2F20+
What fraction of the job did A and B together
get done in 3 hrs?
+3+%2F+%2820%2F3%29+=+9%2F20+
That leaves +1+-+9%2F20+=+11%2F20+
of the job left
Now B working alone completes +11%2F20+
of the job in +8.25+ hrs
+b+=+%28+11%2F20+%29+%2F+%2833%2F4%29+=+%2811%2F20%29%2A%284%2F33%29+
+b+=+1%2F15+
and, since
+a+%2B+b+=+3%2F20+
+a+=+3%2F20+-+1%2F15+
+a+=+9%2F60+-+4%2F60+
+a+=+5%2F60+
+A+=+1%2F12+
B's rate alone is 1 job in 15 hours
A's rate alone is 1 job in 12 hours