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Dorothy and Rosanne are baking cookies for a party. Working alone, Rosanne can finish the cookies in 6 hours. Dorothy can finish them in 8 hours if she is working alone. How long will it take them to bake the cookies if they are working together? Round your answer to the nearest hundredth if necessary.

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josebarradas1607

Answer:

It will take them 3.43 hours.

Step-by-step explanation:

Let T denote the total cookies that need to be cocked. Observe that:

  1. If Rosanne finishes the cookies in 6 hours, that means that she can make [tex]\frac{T}{6}[/tex] cookies per hour.
  2. If Dorothy finishes the cookies in 8 hours, that means that she can make [tex]\frac{T}{8}[/tex] cookies per hour.

Then, by 1) and 2), if they work together would we able to make

[tex]\frac{T}{6}+\frac{T}{8}=\frac{8T+6T}{48}=\frac{14}{48}T=\frac{7}{24}T[/tex]

cookies per hour.

Therefore, in order to finish the T cookies they will need [tex]\frac{24}{7}\approx3.43 hours[/tex]

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