SOLUTION: A machine can fill 1000 cases of soda cans in 3 hours. a second machine requires 5 hours to fill the same amount. how long will it take both machines to fill an order of 5000 cases

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Question 126557This question is from textbook Pre-Algebra
: A machine can fill 1000 cases of soda cans in 3 hours. a second machine requires 5 hours to fill the same amount. how long will it take both machines to fill an order of 5000 cases? This question is from textbook Pre-Algebra

Found 2 solutions by ankor@dixie-net.com, marcsam823:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A machine can fill 1000 cases of soda cans in 3 hours. a second machine requires 5 hours to fill the same amount. how long will it take both machines to fill an order of 5000 cases?
:
Let t = time required when machines work together:
:
Let the completed job = 1 (Filling 1000 cases)
:
+ = 1
:
15* + 15* = 15(1)
:
5t + 3t = 15
:
8t = 15
t =
t = 1.875 hrs to fill 1000 cases
:
But wait, they want the time to fill 5000 cases:
:
5 * 1.875 = 9.375 hrs or 9 hrs 22.5 min

Answer by marcsam823(57) (Show Source):
You can put this solution on YOUR website!
Machine 1:
1. can fill 1000 cases of soda in 3 hours, therefore:
2. can fill 5000 cases of soda in 15 hours
3. can perform 1/15 of this job in one hour
Machine 2:
1. can fill 1000 cases of soda in 5 hours, therefore:
2. can fill 5000 cases of soda in 25 hours
3. can perform 1/25 of this job in one hour
In one hour the two machines working together can perform or or of the job.

Let x = the number of hours required for Machine 1 and Machine 2 to fill 5000 cases.
The number of hours (x) multiplied by the part of the job completed in 1 hour equals the total job completed (1 or 100%)
Set up the equation:

Find lowest common denominator:

Add:

Solve:

Together the machines can perform this job in hours or about 9 hours and 22 minutes.