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### Maths Time Puzzle

Maths Time Puzzle - 17 September

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 9 hours.

What fraction of the tank (initially empty) will be filled in 0.64 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).

1. 1.00

In one hour,

the large inlet pipe fills 1 / 1 of the tank;
the small inlet pipe fills 1 / 5 of the tank;
the outlet pipe empties 1 / 6 of the tank; and therefore
all three pipes together fill [ (1 / 1) + (1 / 5) − (1 / 6) ] of the tank.

Fraction of the tank that will be filled in 0.97 hours =

0.97 [ (1 / 1) + (1 / 5) − (1 / 6) ] = 1.00.

2. 0.66

the large inlet pipe fills 1 / 1 of the tank;
the small inlet pipe fills 1 / 5 of the tank;
the outlet pipe empties 1 / 6 of the tank; and therefore
all three pipes together fill [ (1 / 1) + (1 / 5) − (1 / 6) ] of the tank.

Fraction of the tank that will be filled in 0.97 hours =

0.64 [ (1 / 1) + (1 / 5) − (1 / 6) ] = 0.66.

3. 0.25

There is a small correction the large inlet pipe fills 1 / 3 of the tank;

now 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = .25

1. Agreed:

The large inlet pipe lets in 1/3 of a tank per hour.
The small inlet pipe lets in 1/6 of a tank per hour.
The outlet pipe lets out 1/9 of a tank per hour.

All three pipes are active for 0.64 (16/25) hours .

Filled = 0.64*(1/3) + 0.64 (1/6) - 0.64 (1/9)
=0.64*(1/3 + 1/6 - 1/9)
=0.64*(6/18 + 3/18 - 2/18)
=0.64(7/18)
=(16/25)*(7/18)
=112/450 = 0.24888888.....

4. in 0.64 hrs small pipe fills 0.64/3 of tank
in 0.64 hrs large pipe fills 0.64/6 of tank
in 0.64 hrs small pipe empties 0.64/9 of tank

so fraction of tank going to fill is:
((0.64/3)+(0.64/6))-(0.64/9)=0.248
i.e. 0.25 approximately

5. Question should have asked "What fraction of the tank will be filled in 3/7 hours" to avoid the decimal numbers.

6. 0.25

large pipe fills 0.64/3 of the tank in 0.64 hours (=0.2133)
small pipe fills 0.64/6 of the tank in 0.64 hours(=0.1066)
tank is emptied 0.64/9 in 0.64 hours (=0.0711)
remaining amount in tank after 0.64 hours = (0.2133+0.1066-0.0711) = 0.2488) ~ 0.25

7. A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 1 hour to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 7 hours. What fraction of the tank (initially empty) will be filled in 0.98 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).