Question

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.

Answer 1

It will take them 3.43 hours.

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
   `(T)/(6)` cookies per hour.
2. If Dorothy finishes the cookies in 8 hours, that means that she can make
   `(T)/(8)` cookies per hour.

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

`(T)/(6)+(T)/(8)=(8T+6T)/(48)=(14)/(48)T=(7)/(24)T`

cookies per hour.

Therefore, in order to finish the T cookies they will need
`(24)/(7)\approx3.43 hours`