SOLUTION: Alan took 4 hours to tile the floor of a room. Gary took 6 hours to tile the floor of the same room. If they worked together, how long would they take to tile the floor of the room

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Alan took 4 hours to tile the floor of a room. Gary took 6 hours to tile the floor of the same room. If they worked together, how long would they take to tile the floor of the room      Log On


   



Question 972584: Alan took 4 hours to tile the floor of a room. Gary took 6 hours to tile the floor of the same room. If they worked together, how long would they take to tile the floor of the room
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
Alan's rate:
[ 1 floor tiled ] / [ 4 hrs ]
Gary's rate:
[ 1 floor tiled ] / [ 6 hrs ]
------------------------
Let +t+ = time in hrs to tile floor
with both working together
+1%2F4+%2B+1%2F6+=+1%2Ft+
Multiply both sides by +12t+
+3t+%2B+2t+=+12+
+5t+=+12+
+t+=+2.4+
convert +.4+ hrs to minutes
+.4%2A60+=+24+
---------------
Working together, it will take them 2 hrs and 24 min to tile floor
---------------
check:
+1%2F4+%2B+1%2F6+=+1%2Ft+
+1%2F4+%2B+1%2F6+=+1%2F2.4+
+.25+%2B+.16667+=+.416667+
+.41667+=+.416667+
close enough