The figure shows 2 completely filled tanks being emptied of the water from 2 different taps. The difference in height between Tank T and Tank U is 24 cm. The taps at Tank T and Tank U were turned on at 16 00 and 16 30 respectively, until both were completely empty. At 20 00, the water level in both tanks was the same. At 22 30, Tank U was completely empty and Tank T was only completely empty at 22 00. If the rate of the flow of water from each tap was constant throughout, what was the height of Tank U?

	Tank T	Tank U
Start time	16 00	16 30
First duration of tap flow	4 h	312
Time at the same height	20 00	20 00
Second duration of tap flow	2 h	212
End time	22 00	22 30

	Tank T	Tank U
Total duration	6 h	6 h
Fraction of the tank filled per hour	16 of Tank T	16 of Tank U
Fraction of the tank filled during second duration	13 of Tank T	512 of Tank U

From 1600 to 22 00: 6h
From 1600 to 20 00: 4h
From 2000 to 22 00: 2h

Tank T:
Total duration = 4 + 2 = 6 h

6 h → 1 Tank T
1 h → ¹₆ Tank T
2 h → 2 x ¹₆ = ¹₃ Tank T

From 16 30 to 22 30: 6 h
From 16 30 to 20 00: 3¹₂ h
From 20 00 to 22 30: 2¹₂ h

Tank U:
Total duration = 3¹₂ + 2¹₂ = 6 h

6 h → 1 Tank U
1 h → ¹₆ Tank U
2¹₂ h → 2¹₂ x ¹₆ = ⁵₁₂ Tank U

Compare the heights of the 2 tanks.
Since the height of the water during the second duration is the same for both tanks, make the numerators of the 2 tanks the same.
¹₃ Tank T = ⁵₁₂ Tank U
⁵₁₅ Tank T = ⁵₁₂ Tank U

Total height of Tank T = 15 u
Total height of Tank U = 12 u

Difference between the height of Tank T and Tank U
= 15 u - 12 u
= 3 u

3 u = 24

1 u = 24 ÷ 3 = 8

Height of Tank U
= 15 u
= 15 x 8
= 120 cm

Answer(s): 120 cm