20. 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.
Let's use the formula:
1 / time together = (1 / time1) + (1 / time2)
where time1 and time2 are the individual times for Rosanne and Dorothy.
1 / time together = (1 / 6) + (1 / 8)
1 / time together = 0.2667
time together = 3.75 hours
Therefore, it will take them approximately 3.75 hours to bake the cookies if they are working together.
To determine how long it will take Dorothy and Rosanne to bake the cookies together, we can use the formula:
1 / (Dorothy's time) + 1 / (Rosanne's time) = 1 / (Time working together)
Let's calculate the values and find the answer:
Dorothy's time = 8 hours
Rosanne's time = 6 hours
1 / 8 + 1 / 6 = 1 / (Time working together)
To solve for the time working together, we can take the reciprocal of both sides:
1 / (Time working together) = 1 / 8 + 1 / 6
Let's simplify the right side of the equation:
1 / 8 + 1 / 6 = (6 / 48) + (8 / 48) = 14 / 48
Now, let's take the reciprocal of both sides:
1 / (Time working together) = 14 / 48
To isolate the "Time working together" term, we can take the reciprocal of both sides again:
Time working together = 48 / 14
Simplifying the fraction:
Time working together = 24 / 7
Therefore, it will take Dorothy and Rosanne approximately 3.43 hours (rounded to the nearest hundredth) to bake the cookies together.