SOLUTION: Solve the problem. Frank can type a report in 3 hours and James takes 4 hours. How long will it take the two of them typing together?

Question 156968: Solve the problem. Frank can type a report in 3 hours and James takes 4 hours. How long will it take the two of them typing together?
Found 2 solutions by gonzo, midwood_trail:
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
frank takes 3 hours to do 1 report.
james takes 4 hours to do 1 report.
common denonimator is 12 hours, so .........
frank takes 12 hours to do 4 reports.
james takes 12 hours to do 3 reports.
in that same amount of time they both do a total of 7 reports.
take the report and divide it into 7 parts.
give frank 4 of them and give james 3 of them.
if frank can do 1 report in 3 hours, then frank will take 4/7 * 3 hours to do 4/7 of a report.
if james can do 1 report in 4 hours, then james will take 3/7 * 4 hours to do 3/7 of a report.
4/7 * 3 = 1.714 hours.
3/7 * 4 = 1.714 hours.
working together with frank doing 4/7 of the report and james doing 3/7 of the report, they will take 1.714 hours to finish the report. that is roughly one hour and 43 minutes.
Answer by midwood_trail(310) (Show Source): You can put this solution on YOUR website!
Solve the problem. Frank can type a report in 3 hours and James takes 4 hours. How long will it take the two of them typing together?
Let's make a table.
..........Rate of work.......Time worked.......Fractional Rate of Job Done
Frank.........1/3................x......................x/3
James.........1/4................x......................x/4
The number 1 will indicate the work they do together in the equation below.
x/3 + x/4 = 1
Solve for x.
Our LCD is 12.
Multiply 12 by every term on both sides of the equation.
Doing so, we now have this:
4x + 3x = 12
7x = 12
x = 12/7
The fraction 12/7 is about 1 hour and 70 minutes.
That's how long it will take both guys to do the job together.

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