<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 one tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. Added to this, a third tap can fill the sink in 325 seconds at its maximum constant rate. If all three taps work together at their respective maximum constant rates, estimate the time it will take to fill the sink. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
100
one tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. Added to this, a third tap can fill the sink in 325 seconds at its maximum constant rate. If all three taps work together at their respective maximum constant rates, estimate the time it will take to fill the sink.
test