Janet can mix a batch of cookie dough in 30 minutes. Miya can mix a batch of cookie dough in 45 minutes. Bella can’t cook, and slows down everybody he works with to half-speed. How many minutes will it take the three of them working together to mix a batch of cookie dough?
Janet's rate ---- 1/30 batches per minute, but with Bella there only 1/60
Miya's rate ---- 1/45 bpm, but with Bella there only 1/90
combined rate = 1/60 + 1/90 + 0 = 1/36
time with all 3 working = 1/(1/36) = 36 minutes
Strange wording and strange question. You mean all 3 have their hands in the same batch of dough?
Just because Bella can't cook would have no effect on his ability to mix dough.
1/T = 1/(2*30) + 1/(2*45).
1/T = 1/60 + 1/90 = 3/180 + 2/180 = 5/180,
T = 180/5 = 36 min.
Or T = 60*90/(60+90) = 36 min.
To solve this problem, we need to find the combined rate at which Janet, Miya, and Bella work.
Let's start by finding the rates at which Janet and Miya work individually. Janet takes 30 minutes to mix a batch of cookie dough, so her work rate is 1/30 batches per minute. Similarly, Miya takes 45 minutes to mix a batch, so her work rate is 1/45 batches per minute.
Now, let's consider the work rate of Bella. It is mentioned that Bella slows down everyone to half-speed. So, if the normal rate for Janet and Miya is 1 batch per minute, Bella's rate is half of that, which is 1/2 batch per minute.
To find the combined rate when they work together, we add up the individual rates. So, the combined rate of Janet, Miya, and Bella is:
1/30 + 1/45 + 1/2 = (3/90) + (2/90) + (45/90) = 50/90 = 5/9 batches per minute
Now, to find how long it will take them working together to mix a batch of cookie dough, we need to take the reciprocal of the combined rate:
1 / (5/9) = 9/5 = 1.8 minutes
Therefore, it will take them 1.8 minutes, or 1 minute and 48 seconds, to mix a batch of cookie dough together.