Maria can build a model train in 7 hours. Anne can build a model train in 5 hours…?

How long would it take them if they work together?

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7 Comments »

  1. [4]
    Let us assume that working together they take t hrs to complete the job
    t/7 +t/5 =1
    5t+7t=35[multiplying both sides by 35]
    12t=35
    t=35/12=2 11/12 hrs=2 hrs 55 minutes
    They would take 2 hrs 55 minutes to complete it

    Comment by sarkar05 — March 30, 2010 @ 1:10 am

  2. this is the shortcut method….
    there is a much longer way, but trust me, its not worth the headaches of understanding…

    A = time it takes one person
    B = time it tkaes the other

    (A*B) / (A+B) = combined time

    (7*5) / (7+5) = 35/12= 2.91666… = 2hours 55 minutes

    Comment by irishpisano — March 30, 2010 @ 1:10 am

  3. Maria’s rate = 1 train / 7 hours
    Anne’s rate = 1 train / 5 hours

    Maria’s rate + Anne’s rate = 12/35 trains/hour
    12/35 = 1/x
    12x = 35
    x = 35/12 hours
    x = 2hours and 55 minutes

    Comment by Some Body — March 30, 2010 @ 1:10 am

  4. 35/12 hours

    Comment by Vu Vo — March 30, 2010 @ 1:10 am

  5. Thd formula is (ab)/(a+b)
    So the answer is:
    (7×5)/(7+5)=2.9h

    Comment by Soroush K — March 30, 2010 @ 1:10 am

  6. This type of problem can be solved by considering the rates of each:

    1/7 the rate of Maria, (she does 1/7 per hour.)
    1/5 the rate for Anne.

    Together their rate is (1/7 + 1/5)

    How long would "it take" them if they work together?

    "it take" means how long will it take them to build 1 modle train.

    Let t = the time for them to build the train.

    t * their rate = 1 train.
    t(1/7 + 1/5) = 1

    t*12/35 = 1

    t = 35/12 hours (or 2 hours and 55 minutes)

    Comment by Peter m — March 30, 2010 @ 1:10 am

  7. In 1 hr, Maria can build 1/7th of the model.
    In 1 hr, Anne can build 1/5th of the model.
    Together, in 1 hr, they both can build 1/7+1/5 of the model.= 12/35 of the model. So, it would take 35/12 hours if they work together.

    Comment by cidyah — March 30, 2010 @ 1:10 am

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