SOLUTION: It takes person A 4 hours less than person B to complete a certain task. Working together, both can complete the task in 8/3hours. How long does it take each person to complete the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes person A 4 hours less than person B to complete a certain task. Working together, both can complete the task in 8/3hours. How long does it take each person to complete the      Log On


   

Question 588034: It takes person A 4 hours less than person B to complete a certain task. Working together, both can complete the task in 8/3hours. How long 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
Let ( 1 task ) / ( t hours ) = B's rate
given:
( 1 task ) / ( t - 4 hours ) = A's rate
+1%2Ft+%2B+1%2F%28+t-4+%29+=+1%2F%288%2F3%29+
+1%2Ft+%2B+1%2F%28+t-4+%29+=+3%2F8+
Multiply both sides by +t%2A%28+t-4+%29%2A8+
+8%2A%28+t-4+%29+%2B+8t++=+3%2At%2A%28+t+-4+%29+
+8t+-+32+%2B+8t+=+3%2A%28+t%5E2+-+4t+%29+
+8t+-32+%2B+8t+=+3t%5E2+-+12t+
+3t%5E2+-+28t+%2B+32+=+0+
Use the quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-28+
+c+=+32+
+t+=+%28-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2-4%2A3%2A32+%29%29%2F%282%2A3%29+
+t+=+%28+28+%2B-+sqrt%28+784+-+384+%29%29+%2F+6+
+t+=+%28+28+%2B-+sqrt%28+400+%29%29+%2F+6+
+t+=+%28+28+%2B+20+%29+%2F+6+ ( ignore the (-) root )
+t+=+48%2F6+
+t+=+8+
It takes B 8 hrs to do the task alone
It takes A +8+-+4+ = 4 hrs to do the task alone
check answer:
+1%2Ft+%2B+1%2F%28+t-4+%29+=+3%2F8+
+1%2F8+%2B+1%2F%28+8-4+%29+=+3%2F8+
++1%2F8+%2B+1%2F4+=+3%2F8+
+1%2F8+%2B+2%2F8+=+3%2F8+
+3%2F8+=+3%2F8+
OK