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.
(1 point)
Responses
7.00 hours
7.00 hours
3.43 hours
3.43 hours
0.29 hours
0.29 hours
14.00 hours
The correct answer is 3.43 hours.
To solve this problem, we need to calculate the combined work rate of Rosanne and Dorothy. Rosanne's work rate is 1/6 and Dorothy's work rate is 1/8.
When working together, their combined work rate is 1/6 + 1/8 = 7/24.
To find the number of hours it will take for them to bake the cookies together, we use the formula:
1 / ((1/6) + (1/8)) = 1 / (7/24) = 24/7 = 3.43 hours.
Therefore, it will take them approximately 3.43 hours to bake the cookies together.