The figure shows 2 completely filled tanks being emptied of the water from 2 different taps. The difference in height between Tank Y and Tank Z is 32 cm. The taps at Tank Y and Tank Z were turned on at 15 00 and 15 30 respectively, until both were completely empty. At 18 00, the water level in both tanks was the same. At 19 30, Tank Z was completely empty and Tank Y was only completely empty at 19 00. If the rate of the flow of water from each tap was constant throughout, what was the height of Tank Z?
|
Tank Y |
Tank Z |
Start time |
15 00 |
15 30 |
First duration of tap flow |
3 h |
212 |
Time at the same height |
18 00 |
18 00 |
Second duration of tap flow |
1 h |
112 |
End time |
19 00 |
19 30 |
|
Tank Y |
Tank Z |
Total duration |
4 h |
4 h |
Fraction of the tank filled per hour |
14 of Tank Y |
14 of Tank Z |
Fraction of the tank filled during second duration |
14 of Tank Y |
38 of Tank Z |
From 1500 to 19 00: 4h
From 1500 to 18 00: 3h
From 1800 to 19 00: 1h
Tank Y:
Total duration = 3 + 1 = 4 h
4 h → 1 Tank Y
1 h →
14 Tank Y
1 h → 1 x
14 =
14 Tank Y
From 15 30 to 19 30: 4 h
From 15 30 to 18 00: 2
12 h
From 18 00 to 19 30: 1
12 h
Tank Z:
Total duration = 2
12 + 1
12 = 4 h
4 h → 1 Tank Z
1 h →
14 Tank Z
1
12 h → 1
12 x
14 =
38 Tank Z
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.
14 Tank Y =
38 Tank Z
312 Tank Y =
38 Tank Z
Total height of Tank Y = 12 u
Total height of Tank Z = 8 u
Difference between the height of Tank Y and Tank Z
= 12 u - 8 u
= 4 u
4 u = 32
1 u = 32 ÷ 4 = 8
Height of Tank Z
= 12 u
= 12 x 8
= 96 cm
Answer(s): 96 cm