Posted by **Kim** on Sunday, June 1, 2008 at 10:08am.

John takes 3 hours longer than Andrew to peel 400 pounds of apples. Together they take 8 hours. How long will it take John to peel 400 pounds by himself

- algebra -
**tchrwill**, Sunday, June 1, 2008 at 4:04pm
This should give you the information you need.

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?

Method 1:

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 - John takes 2 hours longer than Andrew to peel 400 pounds of apples. If ...
- math - john takes 3hours longer than andrew to peel 400 pounds of apples. if ...
- algebra - Jonathan and Bill need to stack firewood. Jonathan can stack 130 ...
- algebra - it john 4 hours to mow a lawn it takes maria 3 hours to mow the same ...
- 12th grade - it takes bill 4 hours to paint a house. it takes john 7 hours to ...
- Pre-Calc - The number of pounds of apples a cannery can produce and the ...
- math - it takes bill 4 hours to paint a house. it takes john 7 hours to paint ...
- math - John can build 7 birdhouses in 5 hours, write an equation that will allow...
- Algebra II - John can clean an attic in 11 hours. DeShawn can clean the same ...
- 10th grade algebra - mary takes 3 hours to mow the yard. it takes sally 5 hours...