How many litres of water were there in the bath when the rate of filling increased from 3L/second to 4L/second?

Question

A bath tub takes 20 seconds to fully fill with water. Initially, the rate of filling was 3L/seconds but later on the rate of filling immediately increased to 4L/seconds. The total capacity of the bath is 72L.

How many litres of water were there in the bath when the rate of filling increased from 3L/second to 4L/second?

The answer should be 24L

Answer 1

The bathtub is 72L. At 3L/s, it would take 24s to fill. At 4L/s, it would take 18s to fill. But it only took 20s. So, what we do is we write and equation in terms of time, t. Suppose t seconds passed before the rate changed and 20-t seconds afterward. Notice that t + (20-t) = 20. The bathtub filled with 3(t) liters beforehand and 4(20-t) liters afterward. Thus, in total, there is 3(t) + 4(20-t) liters in the tub. Since we know there is 72L in the tub, we have that 3(t) + 4(20-t) = 72. Now, we solve for t.

Here we go.

We have 3(t) + 4(20-t) = 72.

Then, 3t + 4(20) - 4t = 72.

Then, 3t + 80 - 4t = 72.

Then, -t + 80 = 72.

Then, -t = -8.

Then, t = 8.

Eight Seconds! The rate changed after eight seconds!

So, how much water was in tub beforehand? Oh, right, it was 3(t) = 3(8) = 24L.

Twenty-four Liters! That's like a bunch, I think.