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A pump can be used to either fill or empty a 3600 m^3 tank.
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15 May 2021, 23:02
15 May 2021, 23:02
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Question Stats:
44% (02:38) correct
55% (02:54) wrong based on 27 sessions
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A pump can be used to either fill or empty a 3600 \(m^3\) tank. The emptying capacity is 10 \(m^3/min\) higher than the filling capacity and it requires 12 more minutes to fill the tank than to empty it.
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Emptying capacity in \(m^3/min\) |
50 |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: A pump can be used to either fill or empty a 3600 m^3 tank.
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16 May 2021, 08:44
16 May 2021, 08:44
1
I think that the answer is A
*capacity : 3600 m^3
rate to fill: x (m^3/min)
time to fill: 3600/x (min)
rate to empty: x + 10 (m^3/min)
time to empty: 3600/(x+10) = time to fill - 12 = (3600/x)-12 = (3600-12x)/x (min)
set "time to empty" expressions equal to each other:
3600/(x + 10) = (3600 - 12x) / x
-> 3600x = 3600x + 36000 - 12x^2 - 120x
-> 12x^2 + 120x - 36000 = 0
-> x^2 + 10x - 3000 = 0
-> x = [-10 +- sqrt(100-(4 * -3000)]/2 = [-10 +- sqrt(100+12000)]/2 = [-10 +- sqrt(12100)]/2 = (-10 +- 110)/2
->-> x = -5 +- 55
->->-> x = 50; x = - 60
x = 50
...so:
*capacity : 3600 m^3
rate to fill: 50 (m^3/min)
time to fill: 72 min
rate to empty: 60 (m^3/min)
time to empty: 60 min
A: emptying capacity in m^3/min = 60
B: 50
Answer: A is greater
*capacity : 3600 m^3
rate to fill: x (m^3/min)
time to fill: 3600/x (min)
rate to empty: x + 10 (m^3/min)
time to empty: 3600/(x+10) = time to fill - 12 = (3600/x)-12 = (3600-12x)/x (min)
set "time to empty" expressions equal to each other:
3600/(x + 10) = (3600 - 12x) / x
-> 3600x = 3600x + 36000 - 12x^2 - 120x
-> 12x^2 + 120x - 36000 = 0
-> x^2 + 10x - 3000 = 0
-> x = [-10 +- sqrt(100-(4 * -3000)]/2 = [-10 +- sqrt(100+12000)]/2 = [-10 +- sqrt(12100)]/2 = (-10 +- 110)/2
->-> x = -5 +- 55
->->-> x = 50; x = - 60
x = 50
...so:
*capacity : 3600 m^3
rate to fill: 50 (m^3/min)
time to fill: 72 min
rate to empty: 60 (m^3/min)
time to empty: 60 min
A: emptying capacity in m^3/min = 60
B: 50
Answer: A is greater
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Re: A pump can be used to either fill or empty a 3600 m^3 tank.
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19 Jun 2021, 17:01
19 Jun 2021, 17:01
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KarunMendiratta wrote:
A pump can be used to either fill or empty a 3600 \(m^3\) tank. The emptying capacity is 10 \(m^3/min\) higher than the filling capacity and it requires 12 more minutes to fill the tank than to empty it.
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Emptying capacity in \(m^3/min\) |
50 |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Here given,
Total capacity of the tank = \(3600 [m]m^3\) [/m]
and we are told that emptying capacity is 10 \(m^3/min\) higher than the filling capacity .
also,
it requires 12 more minutes to fill the tank than to empty it.
So,
Time difference = filling time - time required to empty
Let, filling rate be x.
>> \(10 = \frac{3600}{x} - \frac{3600}{(x + 10)}
\)
Doing some math,
>> \(x^2 + 10x - 3000 = 0\)
upon solving,
\(x = -60, 50\)
since, capacity cant be negative, simply we can discarded negative value.
Hence, filling capacity = 50
emptying capacity = 60
Hence, Quantity A is greater.
