SOLUTION: A father and his son clean the house together in 6 hours. When son works alone, it take him an hour longer to clean than his dad alone. Find out how long it takes the son to clean

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A father and his son clean the house together in 6 hours. When son works alone, it take him an hour longer to clean than his dad alone. Find out how long it takes the son to clean       Log On


   

Question 971683: A father and his son clean the house together in 6 hours. When son works alone, it take him an hour longer to clean than his dad alone. Find out how long it takes the son to clean alone.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of cleaning to get their
rate cleaning together
Let +t+ = dad's time in hrs to clean house
working alone
+t+%2B+1+ = son's time in hrs to clean house
working alone
---------------------
In words:
[ 1 house cleaned ] / [ t hrs ] + [ 1 house cleaned ] / [ t + 1 hrs ] =
[ 1 house cleaned ] / [ 6 hrs ]
-----------------------------------
+1%2Ft+%2B+1%2F%28+t+%2B+1+%29+=+1%2F6+
Multip[ly both sides by +t%2A%28+t%2B1+%29%2A6+
+%28+t%2B1+%29%2A6+%2B+6t+=+t%2A%28+t%2B1+%29+
+6t+%2B+6+%2B+6t+=+t%5E2+%2B+t+
+t%5E2+-+11t+-+6+=++0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-11+
+c=+-6+
+t+=+%28+-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2+-+4%2A1%2A%28-6%29+%29%29+%2F+%282%2A1%29+
+t+=+%28+11+%2B-+sqrt%28+121+%2B+24+%29%29+%2F+2+
+t+=+%28+11+%2B-+sqrt%28+145+%29%29+%2F+2+
+t+=+%28+11+%2B+12.042+%29+%2F+2+
+t+=+23.042+%2F+2+
+t+=+11.521+
and
+t+%2B+1+=+12.521+
+.521%2A60+=+31.26+
Working alone, the son takes about 12 hrs 31 min
check:
+1%2Ft+%2B+1%2F%28+t+%2B+1+%29+=+1%2F6+
+1%2F11.521+%2B+1%2F12.521+=+1%2F6+
+.0868+%2B+.0799+=+.16667+
+.1667+=+.16667+
close enough