SOLUTION: If diana can finish a job in 8 hours and natalie can do a job in 10 hours what fraction of the job would be completed if they worked together for 2 hours?

Question 593934: If diana can finish a job in 8 hours and natalie can do a job in 10 hours what fraction of the job would be completed if they worked together for 2 hours?
Answer by AnlytcPhil(1806) (Show Source): You can put this solution on YOUR website!
If diana can finish a job in 8 hours and natalie can do a job in 10 hours what fraction of the job would be completed if they worked together for 2 hours?

Make this chart

            Number of jobs       Time         Rate
            or fraction           in           in
              thereof            hours      jobs/hour
Diana
Natalie
Together

>>...Diana can finish a job in 8 hours...<<

That says Diana can finish ONE job in 8 hours so we fill 1 in
for the number of jobs or fraction thereof, and 8 for the
number of hours:

            Number of jobs       Time         Rate
            or fraction           in           in
              thereof            hours      jobs/hour
Diana            1                 8
Natalie
Together

>>...Natalie can do a job in 10 hours...<<

That says Natalie can finish ONE job in 10 hours so we fill 1 in
for the number of jobs or fraction thereof, and 10 for the
number of hours:

            Number of jobs       Time         Rate
            or fraction           in           in
              thereof            hours      jobs/hour
Diana            1                 8
Natalie          1                10 
Together

Next we filli in the rates in jobs/hour by dividing the number of
jobs by the hours.

            Number of jobs       Time         Rate
            or fraction           in           in
              thereof            hours      jobs/hour
Diana            1                 8          1/8
Natalie          1                10         1/10 
Together

To find their rate together we just add their rates (sort of like 
adding the rate of the river to the rate of the boat in other word
problems.)

So to get their together rate we add 

1/8 + 1/10 = 5/40 + 4/40 = 9/40 jobs/hour

So we fill that in for their together rate.

            Number of jobs       Time         Rate
            or fraction           in           in
              thereof            hours      jobs/hour
Diana            1                 8          1/8
Natalie          1                10         1/10 
Together                                     9/40

>>...what fraction of the job would be completed if they worked
together for 2 hours?...<<

Fill in 2 hours for the time together:


            Number of jobs       Time         Rate
            or fraction           in           in
              thereof            hours      jobs/hour
Diana            1                 8          1/8
Natalie          1                10         1/10 
Together                           2         9/40

To find the fraction of a job just multiply jobs/hour by hours.

         2 � (9/40) = 18/40 = 9/20.

Answer: 9/20ths

The finished chart:

            Number of jobs       Time         Rate
            or fraction           in           in
              thereof            hours      jobs/hour
Diana            1                 8          1/8
Natalie          1                10         1/10 
Together       9/20                2         9/40

Edwin

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