Posted by **elza** on Friday, July 29, 2011 at 8:20pm.

Barry can do a certain job in 9 hours, whereas it takes Samuel 12 hours to do the same job. How long would it take them to do the job working together?

- elementary and intermediate algebra -
**tchrwill**, Saturday, July 30, 2011 at 8:52am
Problems of this type are solvable by means of the following.

If it takes one person 5 hours to paint a room and another person 3 hours, how long will it take to paint the room working together?

1--A can paint a room in 5 hours.

2--B can paint a room in 3 hours.

3--A's rate of painting is 1 room per A hours (5 hours) or 1/A (1/5) room/hour.

4--B's rate of painting is 1 room per B hours (3 hours) or 1/B (1/3) room/hour.

5--Their combined rate of painting is therefore 1/A + 1/B = (A+B)/AB = (1/5 + 1/3) = (8/15) rooms /hour.

6--Therefore, the time required for both of them to paint the 1 room working together is 1 room/(A+B)/AB rooms/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - Generally speaking (if the derivation is not specifically required), if it takes one person A units of time and another person B units of time to complete a specific task working alone, the time it takes them both to complete the task working together is T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.

You might like to derive the equivalant expression involving 3 people working alone and together which results in T = ABC/(AB + AC + BC).

## Answer This Question

## Related Questions

- Math - Barry can do a certain job in 3 hours, whereas it takes Sanchez 5 hours ...
- math - Alex takes 3 hours longer to complete a certain job than Barry does. If ...
- math - A father can do a job in a certain number of hours. His son takes twice ...
- math - 8 workers together at the same rate finished a painting job in 5 hours. ...
- Math - Alice can complete a certain job in 5 hours she had been working on the ...
- college algebra word problem - Wayne can do a job in 6 hours, while Susan can do...
- Algebra - One painter can finish a certain job 5 hours before another painter ...
- Algebra, URGENT!!! - 1) Mio can build a large shed in 15 days less than Yuuko ...
- math - 1.A father can do a job in a certain number of hours. His son takes twice...
- College Algebra - It takes Todd 3 hours longer than Tom to paint a 4x5 feet ...

More Related Questions