SOLUTION: Sofia can type the work in 10 hours. Noga can do it in 15 hours. They work together for 4 hours. Then Sofia left and Noga finished the job. How long did it take

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Sofia can type the work in 10 hours. Noga can do it in 15 hours. They work together for 4 hours. Then Sofia left and Noga finished the job. How long did it take      Log On


   

Question 1057934: Sofia can type the work in 10 hours. Noga can do it in 15 hours. They work together for 4 hours. Then Sofia left and Noga finished the job. How long did it take
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get
their rate working together
Sofia's rate:
[ 1 job ] / [ 10 hrs ]
Noga's rate:
[ 1 job ] / [ 15 hrs ]
---------------------
Let +x+ = the fraction of the job they
get done in 4 hrs
+1%2F10+%2B+1%2F15+=+x%2F4+
Multiply both sides by +60+
+6+%2B+4+=+15x+
+15x+=+10+
+x+=+2%2F3+
----------------------
2/3 of the job got done, so 1/3 is left
Noga finished the job.
Let +t+ = time in hrs for her to finish
+1%2F15+=+%28%281%2F3%29%29+%2F+t+
+1%2F15+=+1%2F%28%283t%29%29+
Multiply both sides by +15t+
+t+=+5+
-----------------
+4+%2B+5+=+9+
The job took 9 hrs