SOLUTION: It takes crew A 4 hours to paint a room. It takes crew B 5 hours to do the same job. How long will it take to paint the room with both crews working together.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes crew A 4 hours to paint a room. It takes crew B 5 hours to do the same job. How long will it take to paint the room with both crews working together.       Log On


   

Question 1030071: It takes crew A 4 hours to paint a room. It takes crew B 5 hours to do the same job. How long will it take to paint the room with both crews working together.
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Crew A's rate of painting:
[ 1 room painted ] / [ 4 hrs ]
Crew B's rate of painting:
[ 1 room painted ] / [ 5 hrs ]
Let +t+ = time in hrs for A and B
to paint the room working together
------------------------------
Add their rates of painting to get
their rate of painting together
+1%2F4+%2B+1%2F5+=+1%2Ft+
Multiply both sides by +20t+
++5t+%2B+4t+=+20+
+9t+=+20+
+t+=+2+%2B+2%2F9+ hrs
Convert hrs to minutes
+%282%2F9%29%2A60+=+13.333+
--------------------
Working together they take
2 hrs 13.333 min to paint the room
-----------------
check:
+1%2F4+%2B+1%2F5+=+1%2Ft+
+1%2F4+%2B+1%2F5+=+1%2F%2820%2F9%29+
+.25+%2B+.2+=+9%2F20+
+.45+=+.45+
OK

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

Here's a way to do it without algebra,
just basic math:

The LCM of 4 hours and 5 hours is 20 hours.

Crew A can paint 5 rooms in 20 hours and 
Crew B can paint 4 rooms in 20 hours.
So working together for 20 hours, they can paint 9 rooms 
So working together, they can 1 room in 1/9 that much time 
1/9th of 20 hours is 20/9 hours or 2 2/9th hours.

Edwin