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Two pools in the shape of rectangular prisms are being fille
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07 Jan 2021, 10:03
07 Jan 2021, 10:03
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Question Stats:
77% (01:38) correct
22% (01:27) wrong based on 22 sessions
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Two pools in the shape of rectangular prisms are being filled with water by pumps. The first pump fills its pool completely in one hour. The second pumps water twice as fast as the first pump, and fills a pool that is twice the width, twice the length, and the same depth of the first pool. How many hours does it take the second pump to fill its pool?
A. 1
B. 2
C. 4
D. 8
E. 16
Kudos for the right answer and explanation
A. 1
B. 2
C. 4
D. 8
E. 16
Kudos for the right answer and explanation
Re: Two pools in the shape of rectangular prisms are being fille
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08 Jan 2021, 07:59
08 Jan 2021, 07:59
2
Let's take Pump 1 and Pump 2
Rectangular prism shaped pool
Take length = l width = b depth = h
Volume of pool 1 = lbh
Pump 1 will take 1 hr to fill the water of volume \(lbh\)
Pool 2 has twice the length and twice the width and same depth
Volume of pool 2 = \((2*l)(2*b)(h)\) = \(4lbh\)
Pump 1 will take with it's speed to fill pool 2, 4 hours.
Now it is given that pump 2 fills twice the water than pump 1. So the speed will be half than the time taken by pump 2.
So Pump 2 will take 2 hours to fill Pool 2.
Answer B
Rectangular prism shaped pool
Take length = l width = b depth = h
Volume of pool 1 = lbh
Pump 1 will take 1 hr to fill the water of volume \(lbh\)
Pool 2 has twice the length and twice the width and same depth
Volume of pool 2 = \((2*l)(2*b)(h)\) = \(4lbh\)
Pump 1 will take with it's speed to fill pool 2, 4 hours.
Now it is given that pump 2 fills twice the water than pump 1. So the speed will be half than the time taken by pump 2.
So Pump 2 will take 2 hours to fill Pool 2.
Answer B
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Re: Two pools in the shape of rectangular prisms are being fille
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03 Feb 2021, 00:18
03 Feb 2021, 00:18
1
For Pump 1:
W1 = Volume of the pool
T1 = 1 hour
R1 = Rate of filling the pool
So, T1 = W1/R1
For Pump 2:
W2 = 4W1 (twice the width and twice the length)
R2 = 2R1 (twice as fast)
So, T2 = W2/R2
T2 = 4W1/2R1 = 2W1/R1 = 2T1 (from above)
So, If pump 1 takes 1 hour then pump 2 will take 2 hours.
Hence, option B
W1 = Volume of the pool
T1 = 1 hour
R1 = Rate of filling the pool
So, T1 = W1/R1
For Pump 2:
W2 = 4W1 (twice the width and twice the length)
R2 = 2R1 (twice as fast)
So, T2 = W2/R2
T2 = 4W1/2R1 = 2W1/R1 = 2T1 (from above)
So, If pump 1 takes 1 hour then pump 2 will take 2 hours.
Hence, option B
