Answer:
12 hours
Step-by-step explanation:
Time taken by pipe A = 24 hours
Time taken by pipe B = 36 hours
Time taken by pipe C = 32 hours
To find:
How long would it take the three pipes to fill the pool if pipe B is turned on 3 hours after pipe A and pipe C is turned on 1 hour after pipe B?
Solution:
First of all, let us assume the total capacity of the pool.
Let us take LCM of 24, 36 and 32.
LCM of 24, 36 and 32 = 288
Let the total capacity of the pool = 288 units
Total units filled by pipe A in one hour = [tex]\frac{288}{24} = 12\ units[/tex]
Total units filled by pipe B in one hour = [tex]\frac{288}{36} = 8\ units[/tex]
Total units filled by pipe C in one hour = [tex]\frac{288}{32} = 9\ units[/tex]
Now, for the first 3 hours, only pipe A operates, so units filled in first three hours = [tex]12\times 3 =36\ units[/tex]
For the next one hour, A and B both operate together, so units filled in the next 1 hour = 12 + 8 = 20 units
Total number of units filled in 4 hours = 36 + 20 = 56 units
Units to be filled to completely fill the pool = 288 - 56 = 232 units
Now, after the 4th hours, all the pipes operate together.
So, number of units filled in each hour = 12 + 8 + 9 = 29 units
Time taken to fill 232 units = [tex]\frac{232}{29} = 8\ hours[/tex]
Total time taken = 4 + 8 = 12 hours
