A bucket is normally filled in 10 hours, but takes 2 hrs longer to fill because of a leak in its bottom. If the bucket is full, the leak will empty it in how many hours ?
Question
A bucket is normally filled in 10 hours, but takes 2 hrs longer to fill because of a leak in its bottom. If the bucket is full, the leak will empty it in how many hours ?
Solution
Let's solve this step by step:
Step 1: Let's denote the rate at which the bucket is filled as 1 bucket per 10 hours, or 1/10 buckets per hour.
Step 2: If the bucket takes 2 hours longer to fill because of the leak, then the combined rate of filling the bucket and the leak emptying it is 1 bucket per 12 hours, or 1/12 buckets per hour.
Step 3: The rate at which the leak empties the bucket is the difference between the rate of filling the bucket and the combined rate. So, the leak empties the bucket at a rate of 1/10 - 1/12 buckets per hour.
Step 4: Simplifying the fraction gives us the rate of the leak as 1/60 buckets per hour.
Step 5: Therefore, the leak will empty a full bucket in 60 hours.
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