im totally clueless?

john and peter, ages 11 and 13, were given a job to do at 9am. working alone, john can do the job in 5 hrs, and peter in 4 hrs. at 10am they went swimming until 1:30, then came back and finished the job. at what time did they finish it?

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  • M
    Lv 6
    1 decade ago
    Favorite Answer

    Working alone, John can do the job in 5 hrs, and Peter in 4 hrs.

    => John can do 1/5 of the work in 1 hour and

    Peter can do 1/4 of the work in one hour.

    So both together will do

    (1/5 + 1/4) of the job in one hour (=60 minutes)

    1/5 + 1/4 = (4+5)/20 = 9/20

    => 9/20 of the job in 60 minutes

    9/20 ·x = 60

    9x = 60·20

    x = 60·20/9

    x = 400/3

    x = 133 1/3

    This means they can both together finish the job in 133 1/3 minutes which is 2 hours, 13 minutes and 20 seconds.

    They worked for 1 hour from 9am till 10am. When they came back from swimming at 1:30, they still had 1 hour, 13 minutes and 20 seconds of work to do.

    Therefore they finished the job at

    2:43 and 20 seconds pm

    Hope this helps.

    (EDIT)

    OMKAR is NOT RIGHT because .23 hours does not equal 23 minutes. An hour has 60 minutes, not 100!

  • 1 decade ago

    Working together, they need 2 hours and 13 1/3 minutes.

    This is how that is determined:

    John works at 5 hours per job, Peter at 4 hours per job.

    So, John works at 1/5 jobs per hour and Peter and 1/4 jobs per hour.

    So, to make this an algebra problem, let X equal the number of hours they need to work together to complete 1 job:

    1/5 X + 1/4 X = 1 job

    4/20 X + 5/20 X = 1 job

    9/20 X = 1 job

    therefore, X = 2 2/9 hours or 2 hours and 13 1/3 minutes

    So, if they started at 9am, took 3.5 hours off in the middle, they would complete in 5 hours 43 1/3 minutes total, or at clock time of 43 1/3 minutes past 2pm.

    Source(s): I have a math degree and teach college calc
  • 1 decade ago

    John at 6:30 Peter at 5:30 I guess

  • 1 decade ago

    HERE!, chill friend

    Take a deep breadth and cool down, my answer is quite simple

    Its simple,

    (first you should know that we assume total work to be '1')

    A/C to question,

    john does the work alone in 5 hours,

    so the work done by john in an hour will be 1/5

    Peter does the work in 4 hours

    So, the work he does in an hour is 1/4

    They had started the work at 9 and stopped at 10

    so they did some work for an hour

    The work done by both of them in an hour,

    = 1/5 +1/4

    = 9/20

    We know the total work is "1"

    so the work that is left is 1 - 9/20

    They again start working at 1.30

    They can do 9/20 of the work in one hour,

    So, the time they'll take to complete the left work(1- 9/20)

    =(1 - 9/20)/9/20

    9/20 = 0.45

    = (1 - 0.45)/ 0.45

    =1.2222222222222222...............

    = 1.23 (approximately)

    We can even express it like this:

    let J be the work done by john in one hour

    and P be the work done by peter in one hour

    and T be the time taken to complete the remaining work

    So,

    (J+P) + T(J + P) = 1

    =>(1 + T) ( J + P ) = 1

    But we know J + P = 9/20

    =>(1 + T) = 20/9

    =>T= 20/9 -1

    T = 1.222222222222222....

    T = 1.23 (approximately)

    so the answer is (1.30 + 1.23)hours

    = 2.53 pm

    (you also have to note that no work is done when they were swimming)

    AND I AM RIGHT

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  • 1 decade ago

    1/(1/5+1/4)=20/9

    20/9-1=11/9

    1:30+11/9h = 2:13:40

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