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.
• 7.00 hours
• 3.43 hours
• 0.29 hours
• 14.00 hours
3.43 hours?
To find out how long it will take Dorothy and Rosanne to bake the cookies together, we can use the concept of work rates.
The work rate is the amount of work done per unit of time. In this case, the work is baking the cookies, and the time unit is hours.
We know that Rosanne takes 6 hours to bake the cookies alone, so her work rate is 1/6 (1 cookie/6 hours). Similarly, Dorothy's work rate is 1/8 (1 cookie/8 hours).
When they work together, their work rates are combined, so we can add their individual work rates to find the total work rate:
1/6 + 1/8 = (4/24) + (3/24) = 7/24
Now, we can use the inverse of the work rate to find how long it will take them to bake the cookies together:
1 / (7/24) = 24/7 ≈ 3.43 hours
Therefore, it will take Dorothy and Rosanne approximately 3.43 hours to bake the cookies together.
The correct answer is:
• 3.43 hours