SOLUTION: Pete can do a piece of work in 6 hours less time than Rick. Together, they can do the work in 9 hours and 12 minutes. How long will each take while working alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pete can do a piece of work in 6 hours less time than Rick. Together, they can do the work in 9 hours and 12 minutes. How long will each take while working alone?       Log On


   

Question 982238: Pete can do a piece of work in 6 hours less time than Rick. Together, they can do the work in 9 hours and 12 minutes. How long will each take while working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+%7C = Rick's time to finish work alone in hours
+t+-+6+ = Pete's time to finish work aone in hours
-----------------
Rick's rate of working:
[ 1 job finished ] / [ t hrs ]
Pete's rate of working:
[ 1 job finished ] / [ t - 6 ]
-----------------------
Convert 12 min to hrs:
+12%2F60+=+.2+ hrs
Add their rates of working to get
their rate working together
+1%2Ft+%2B+1%2F%28+t-6+%29+=+1%2F9.2+
Multiply both sides by +9.2%2At%2A%28+t-6+%29+
+9.2%2A%28+t-6+%29+%2B+9.2t+=+t%2A%28+t-6+%29+
+9.2t+-+55.2+%2B+9.2t+=+t%5E2+-+6t+
+t%5E2+-+18.4t+-+6t+%2B+55.2+=+0+
+t%5E2+-+24.4t+%2B+55.2+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-24.4+
+c+=+55.2+
+t+=+%28+-%28-24.4%29+%2B-+sqrt%28+%28-24.4%29%5E2+-+4%2A1%2A55.2+%29%29+%2F+%282%2A1%29+
+t+=+%28+24.4+%2B-+sqrt%28+595.36+-+220.8+%29%29+%2F+2+
+t+=+%28+24.4+%2B-+sqrt%28+374.56+%29%29+%2F+2+
+t+=+%28+24.4+%2B+19.354+%29%2F2+
+t+=+43.754%2F2+
+t+=+21.877+
and
+t+-+6+=+15.877+
--------------------
Rick takes 21.877 hrs working aloine
Pete takes 15.877 hrs working alone
--------------------
check:
+1%2Ft+%2B+1%2F%28+t-6+%29+=+1%2F9.2+
+1%2F21.877+%2B+1%2F15.877+=+1%2F9.2+
+.04571+%2B+.06298+=+.1087+
+.10869+=+.1087+
close enough
Hope I got it!