SOLUTION: A crew of 2 could put siding on a house in 30 hours. Another crew of 3 could do the same job in 24 hours. How long would it take all 5 people working together?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A crew of 2 could put siding on a house in 30 hours. Another crew of 3 could do the same job in 24 hours. How long would it take all 5 people working together?       Log On


   

Question 1157207: A crew of 2 could put siding on a house in 30 hours. Another crew of 3 could do the same job in 24 hours. How long would it take all 5 people working together?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of working for the crew of 2 is:
[ 1 siding job ] / [ 30 hrs ]
The rate of working for the crew of 3 is:
[ 1 siding job ] / [ 24 hrs ]
Add their rates to get rate working together
Let +t+ = time in hrs for both crews to
do the job
------------------------
+1%2F30+%2B+1%2F24+=+1%2Ft+
multiply both sides by +120t+
+4t+%2B+5t+=+120+
+9t+=+120+
+t+=+13.333+
+.333%2A60+=+20+
All 5 working together take 13 hrs 20 min
------------------------------
+.0333+%2B+.041667+=+1%2Ft+
+.075+=+9%2F120+
+.075+=+.075+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is alternative to the standard algebraic solution method shown by the other tutor.

Consider the least common multiple of the two given times: the LCM of 24 and 30 is 120.

In 120 hours, the crew of 2 could put siding on 120/30 = 4 houses; the crew of 3 could put siding on 120/24 = 5 houses. So in 120 hours the two crews together could put siding on 4+5=9 houses.

So the number of hours it would take the two crews together to put siding on 1 house is 120/9 = 40/3, or 13 1/3 hours, or 13 hours 20 minutes.