### Two taps A and B can fill a water tank in 5 and 4 hours respectively. If they are turned up alternatively for one hour each (starting with tap A), find the time taken to fill the tank.

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**Answer: **4.5 hours

**Step by Step Explanation: **- Tap A takes 5 hours to fill the water tank. So in 1 hour it will fill of the tank.
- Tap B takes 4 hours to fill the water tank. So in 1 hour it will fill of the tank.
- The tank is filled by each tap in alternate hours, starting with the tap A. So in the first hour, of the tank will be filled, and in the second hour an additional of the tank will be filled.
- We have to find out the number of hours required to fill the whole tank.
- So + + + + ..... = 1

When this value equals to one, we get the number of hours the tank was filled in. - Let m be the group of days (each group having 2 hours - 1 for tap A and 1 for tap B) which are needed to fill the tank).

From above, we can write m( + ) = 1

=> m = = 2.25 - Since m is group of 2 hours, it will 2 x m hours to fill the tank. The tank will be filled in 4.5 hours.