SOLUTION: In 5 min a conveyor belt moves 400 pounds of cans to a storage area. A smaller belt moves the same quantity of cans the same distance in 9 minutes. How long does it take if belts a

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: In 5 min a conveyor belt moves 400 pounds of cans to a storage area. A smaller belt moves the same quantity of cans the same distance in 9 minutes. How long does it take if belts a      Log On


   

Question 697544: In 5 min a conveyor belt moves 400 pounds of cans to a storage area. A smaller belt moves the same quantity of cans the same distance in 9 minutes. How long does it take if belts are used
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of moving cans to get
their rate moving them together.
1st belt:
Rate = ( 400 lbs of cans ) / ( 5 min )
2nd belt:
Rate = ( 400 lbs of cans ) / ( 9 min )
-------------------------------
Let +t+ = time in minutes to move
400 cans with both belts used
Call 400 cans " 1 job "
+1%2F5+%2B+1%2F9+=+1%2Ft+
Multiply both sides by +45t+
++9t+%2B+5t+=+45+
+14t+=+45+
+t+=+3.2143+ min
Both belts can move 400 cans in 3.2143 min
check:
+1%2F5+%2B+1%2F9+=+1%2Ft+
+.2+%2B+.1111+=+1%2F3.2143+
+.3111+=+1%2F3.2143+
+1.0000044+=+1+
OK- error due to rounding off