SOLUTION: Jack can wash dishes in 30 minutes and Jill can wash them in 25 minutes. After Jack has been working for 10 minutes, Jill begins to help him. How long will it take both to finish t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack can wash dishes in 30 minutes and Jill can wash them in 25 minutes. After Jack has been working for 10 minutes, Jill begins to help him. How long will it take both to finish t      Log On


   

Question 955114: Jack can wash dishes in 30 minutes and Jill can wash them in 25 minutes. After Jack has been working for 10 minutes, Jill begins to help him. How long will it take both to finish the dishes?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Jack's rate is:
+1%2F30+ dishes/minutes
+%28+1%2F30+%29%2A10+=+1%2F3+ of the dishes
Jack cleans 1/3 of the dishes in +30+ min
That means there is +2%2F3+ of the dishes remaining
--------------------------------------
Add their rates to find time +t+ in minutes to
clean the remaining +2%2F3+ of the dishes
+1%2F30+%2B+1%2F25+=+%28%282%2F3%29%29+%2F+t+
Multiply both sides by +150t+
+5t+%2B+6t+=+100+
+11t+=+100+
+t+=+9.091+
It will take them 9.091 min
+1%2F30+%2B+1%2F25+=+%28%282%2F3%29%29+%2F+%28%28+100%2F11%29%29+
+1%2F30+%2B+1%2F25+=+22%2F300+
Multiply both sides by +300+
+10+%2B+12+=+22+
+22+=+22+
OK