SOLUTION: one person can complete a task 8 hours sooner than another person. working together both people can perform the task in 3 hours. How many does it take each person to complete the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: one person can complete a task 8 hours sooner than another person. working together both people can perform the task in 3 hours. How many does it take each person to complete the       Log On


   

Question 873130: one person can complete a task 8 hours sooner than another person. working together both people can perform the task in 3 hours. How many does it take each person to complete the task working alone?
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
-----------
1st person's rate:
( 1 task ) / ( t - 8 hrs )
where (t) is in hours
-------------------
2nd person's rate:
( 1 task ) / ( t hrs )
-----------------
Rate working together:
( 1 task ) / ( 3 hrs )
--------------------
+1%2F%28+t+-+8+%29+%2B+1%2Ft+=+1%2F3+
Multiply both sides by +%28+t-8+%29%2At%2A3+
+3t+%2B+3%2A%28+t-8+%29+=+t%2A%28+t-8+%29+
+3t+%2B+3t+-+24+=+t%5E2+-+8t+
+t%5E2+-+14t++=+-24+
------------------------
complete the square
+t%5E2+-+14t+%2B+%28+14%2F2+%29%5E2+=+-24+%2B+%2814%2F2%29%5E2+
+t%5E2+-+14t+%2B+49+=+-24+%2B+49+
+%28+t+-+7+%29%5E2+=+25+
+%28+t+-+7+%29%5E2+=+5%5E2+
+t+-+7+=+5+
+t+=+12+
+t+-+8+=+4+
-------------
The 1st person takes 4 hrs
The 2nd person takes 12 hrs
-------------------------
check answer:
+1%2F%28+t+-+8+%29+%2B+1%2Ft+=+1%2F3+
+1%2F%28+12+-+8+%29+%2B+1%2F12+=+1%2F3+
+1%2F4+%2B+1%2F12+=+1%2F3+
+3%2F12+%2B+1%2F2+=+4%2F12+
+4%2F12+=+4%2F12+
OK