Question:medium
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
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Break the work at the switching point. Compute time for each phase using \(\text{time}=\frac{\text{work}}{\text{rate}}\) and add them.
Updated On: Jul 16, 2026
- 3 hours 15 min
- 3 hours 45 min
- 3 hours 40 min
- 3 hours 50 min
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: One tap fills the whole tank in 6 hours, so it fills half the tank in \(\dfrac{6}{2}=3\) hours.
Step 2: For the second half, 4 taps work together (the original one plus 3 more), so the combined rate is 4 times a single tap's rate, meaning the same amount of work now takes \(\dfrac{1}{4}\) of the time a single tap would need for it: \(\dfrac{3\ \text{hours}}{4}=45\) minutes.
Step 3: Adding both stages, total time \(=3\ \text{hours}+45\ \text{minutes}\). \[ \boxed{3\ \text{hours } 45\ \text{minutes}} \]
Step 2: For the second half, 4 taps work together (the original one plus 3 more), so the combined rate is 4 times a single tap's rate, meaning the same amount of work now takes \(\dfrac{1}{4}\) of the time a single tap would need for it: \(\dfrac{3\ \text{hours}}{4}=45\) minutes.
Step 3: Adding both stages, total time \(=3\ \text{hours}+45\ \text{minutes}\). \[ \boxed{3\ \text{hours } 45\ \text{minutes}} \]
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