### 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.

4.5 hours

Step by Step Explanation:
1. Tap A takes 5 hours to fill the water tank. So in 1 hour it will fill
 1 5
of the tank.
2. Tap B takes 4 hours to fill the water tank. So in 1 hour it will fill
 1 4
of the tank.
3. The tank is filled by each tap in alternate hours, starting with the tap A. So in the first hour,
 1 5
of the tank will be filled, and in the second hour an additional
 1 4
of the tank will be filled.
4. We have to find out the number of hours required to fill the whole tank.
5. So
 1 5
+
 1 4
+
 1 5
+
 1 4
+ ..... = 1
When this value equals to one, we get the number of hours the tank was filled in.
6. 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 5
+
 1 4
) = 1
=> m =
 5 x 4 5 + 4
= 2.25
7. 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. 