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.
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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