Question

A tap can fill a bucket in 6 hours. After half the bucket is filled, three more similar taps are opened. What is the total time taken to fill the bucket completely?.

Answer 1

The total time taken to fill the bucket completely is 3 hours 45 minutes

The time taken to fill the bucket by one tap= 6 hours

Then the time take by one tap to fill half of the bucket= 3 hours

Part filled by one tap in one hour =$\frac{1}{6}$

Part filled by four taps in one hour =$4(\frac{1}{6})=\frac{4}{6}=\frac{2}{3}$

Given, that after half the bucket is filled, three more similar taps are opened

Then the remaining part = $1-\frac{1}{2}=\frac{1}{2}$

Time taken to fill the half of the bucket= $(\frac{1}{2} )(\frac{2}{3})=\frac{3}{4}$ hours

Convert the hours to minutes

$(\frac{3}{4})60=45$ minutes

Therefore,

Total time taken to fill the bucket= The time taken by one tap to fill half of the bucket+  Time taken by 4 taps to fill the half of the bucket

=3 hours+ 45 minutes

=3 hours 45 minutes

Hence, The total time taken to fill the bucket completely is 3 hours 45 minutes

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