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-A baker can decorate the day's cookie supply four times as fast as his new assistant. If they decorate all the cookies working together in 28 minutes, how long would it take for each of them to decorate the cookies
Working individually?

Question

Quizplus · Accepted Answer

Let's assume that the new assistant takes x minutes to decorate all the cookies alone.
Then the baker can decorate all the cookies in x/4 minutes.
Now, if they work together, they can decorate all the cookies in 28 minutes.
Using the formula: (time taken by A * time taken by B) / (time taken by A + time taken by B) = Total time
we can find x as:
(x * x/4) / (x/4 + x) = 28
Solving this equation, we get x = 112 minutes
So, the baker takes 28 minutes / 4 = 7 minutes to decorate all the cookies alone.
Therefore, the answer would be:
A) 11ebb63d_1b61_da39_b851_5913bd83e1aa_TB8475_11 - Incorrect, as it doesn't match with the calculations.
B) 11ebb63d_1b61_da3a_b851_11e4ed93110a_TB8475_11 - Correct, as the assistant takes 112 minutes and the baker takes 7 minutes to decorate all the cookies alone.
C) 11ebb63d_1b61_da3b_b851_d9239ca75b6e_TB8475_11 - Incorrect, as it doesn't match with the calculations.
D) 11ebb63d_1b62_014c_b851_5fe8afb5255c_TB8475_11 - Incorrect, as it doesn't match with the calculations. Let the time taken by the assistant be x minutes. Then the time taken by the baker will be x/4 minutes. Together they take 28 minutes to decorate all the cookies. So, their combined rate of work is 1/28. Using the formula "rate x time = work", we can write:
(x/4) + x = 1/28
Solving this equation gives x = 40 minutes (approx) for the assistant, and x/4 = 10 minutes (approx) for the baker. Therefore, the answer is B, as 10 minutes is the time taken by the baker to decorate all the cookies working individually. And the assistant takes 40 minutes to decorate all the cookies working individually.

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