SOLUTION: Pete can do a job in 4 hours less than Sam can. Working together,they can complete the job in 16 hours. How long would it take each working alone? Round your answer to the nearest

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Pete can do a job in 4 hours less than Sam can. Working together,they can complete the job in 16 hours. How long would it take each working alone? Round your answer to the nearest       Log On


   

Question 967061: Pete can do a job in 4 hours less than Sam can. Working together,they can complete the job in 16 hours. How long would it take each working alone? Round your answer to the nearest tenth of an hour
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working
Let +t+ = time it takes Sam to do job
[ 1 job ] / [ t hrs ] = rate for Sam
[ 1 job ] / [ t - 4 hrs ] = rate for Pete
[ 1 job ] / [ 16 hrs ] = their rate working together
----------------------
+1%2Ft+%2B+1%2F%28+t-4+%29+=+1%2F16+
Multiply both sides by +t%2A%28+t-4+%29%2A16+
+16%2A%28+t-4+%29+%2B+16t+=+t%2A%28+t-4+%29+
+16t+-+64+%2B+16t+=+t%5E2+-+4t+
+t%5E2+-+36t+%2B+64+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-36+
+c+=+64+
You can finish. Find +t+
and +t+%2B+4+