Question

In a certain bathtub both the cold water and the hot water fixtures leak the cold water leak alone would fill an empty bucket in c hours and the hot water leak alone would fill the same bucket in h hours where c

Answer 1

Here, I have presented the completion of your question from where it has abruptly cut down.  

The remaining question is “where c<h. which answer from the given options is correct when the both fixtures begun to leak at the same time to fill a bucket in t hours.""

The options are

I.  0 < t < h  

II. c < t < h  

III. c/2 < t < h/2  

Answer:

I. 0 < t < h. That is always correct, because the time that is needed both fixtures to fill the bucket is less than the time needed for the both fixtures to fill the bucket one by one.

II. c < t < h. That cannot be correct as the time required for the two fixtures to fill the bucket seems greater than the time required for the fixtures to fill the bucket one by one.

III. c/2 < t < h/2. This sequence is always correct. we can use algebra to prove this.  

Here, in this case, both I and III are correct.