Problem:
Two water taps together can fill a tank in 9⅜ hours. The time it takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Solution:

Let's assume the time taken by the smaller tap to fill the tank alone is 'x' hours.

Time taken by the larger tap to fill the tank alone:
According to the given information, the time taken by the larger tap to fill the tank alone is 10 hours less than the smaller tap. So, the time taken by the larger tap is (x - 10) hours.

Rate of filling the tank:
The rate at which the smaller tap fills the tank = 1/x tanks per hour.
The rate at which the larger tap fills the tank = 1/(x - 10) tanks per hour.

Combined rate of filling the tank:
When both taps are open, their rates of filling the tank are added together.
So, the combined rate of filling the tank = 1/x + 1/(x - 10) tanks per hour.

Time taken by both taps together:
According to the problem, both taps together can fill the tank in 9⅜ hours.
Converting 9⅜ hours to an improper fraction:
9⅜ = 9 + 3/8 = 72/8 + 3/8 = 75/8 hours.

Now, we can use the formula:
Time = 1 / Rate

Therefore, 75/8 = 1 / (1/x + 1/(x - 10))

Solving the equation:
To solve this equation, we can multiply both sides by (x)(x - 10)(8) to eliminate the denominators.

75(x)(x - 10) = 8[(x - 10) + x]

75x(x - 10) = 8(2x - 10)

75x^2 - 750x = 16x - 80

75x^2 - 766x + 80 = 0

Using the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / 2a

Plugging in the values:
x = [-(-766) ± √((-766)^2 - 4(75)(80))] / (2)(75)

Simplifying the equation:
x = [766 ± √(588244 - 24000)] / 150

x = [766 ± √564244] / 150

Simplifying further:
Using a calculator, we find that the square root of 564244 is approximately 751.21.

x = [766 ± 751.21] / 150

x ≈ [766 + 751.21] / 150 ≈ 10.11 hours or x ≈ [766 - 751.21] / 150 ≈ 0.98 hours

Final Answer:
Therefore, the time taken by the smaller tap to fill the tank alone is approximately 0.98 hours, and the time taken by the larger tap to fill the tank alone is approximately 10.11 hours.