The figure shows 2 completely filled containers being emptied of the water from 2 different taps. The difference in height between Container T and Container U is 15 cm. The taps at Container T and Container U were turned on at 15 00 and 15 30 respectively, until both were completely empty. At 19 00, the water level in both tanks was the same. At 21 30, Container U was completely empty and Container T was only completely empty at 21 00. If the rate of the flow of water from each tap was constant throughout, what was the height of Container U?
|
Container T |
Container U |
Start time |
15 00 |
15 30 |
First duration of tap flow |
4 h |
312 |
Time at the same height |
19 00 |
19 00 |
Second duration of tap flow |
2 h |
212 |
End time |
21 00 |
21 30 |
|
Container T |
Container U |
Total duration |
6 h |
6 h |
Fraction of the container filled per hour |
16 of Container T |
16 of Container U |
Fraction of the container filled during second duration |
13 of Container T |
512 of Container U |
From 1500 to 21 00: 6h
From 1500 to 19 00: 4h
From 1900 to 21 00: 2h
Container T:
Total duration = 4 + 2 = 6 h
6 h → 1 Container T
1 h →
16 Container T
2 h → 2 x
16 =
13 Container T
From 15 30 to 21 30: 6 h
From 15 30 to 19 00: 3
12 h
From 19 00 to 21 30: 2
12 h
Container U:
Total duration = 3
12 + 2
12 = 6 h
6 h → 1 Container U
1 h →
16 Container U
2
12 h → 2
12 x
16 =
512 Container U
Compare the heights of the 2 containers.
Since the height of the water during the second duration is the same for both containers, make the numerators of the 2 tanks the same.
13 Container T =
512 Container U
515 Container T =
512 Container U
Total height of Container T = 15 u
Total height of Container U = 12 u
Difference between the height of Container T and Container U
= 15 u - 12 u
= 3 u
3 u = 15
1 u = 15 ÷ 3 = 5
Height of Container U
= 15 u
= 15 x 5
= 75 cm
Answer(s): 75 cm