Machines A and B each assembled 3,000 metal clips in 15 hours and 12 hours, respectively, working alone at their constant rates. On Monday, working simultaneously at their respective constant rates, the two machines assembled a total of n clips in x hours. The next day, machine A was modified so that its constant rate decreased by 25 percent. If the two machines worked simultaneously at their respective constant rates for x hours after the modification of machine A, then the total number of clips that they assembled in x hours was approximately what percent less than it was the day before?
A) 6%
B) 11%
C) 16%
D) 20%
E) 25%
A pump delivered water to fill an empty swimming pool. The pump delivered the water at a constant rate of 450 liters per minute until the pool was half full. Then the pump became partially clogged and delivered the water at a slower constant rate until the pool was full. For the whole time during which the pump delivered water to fill the empty pool, its average rate was 360 liters per minute. What was the pump's slower constant rate, in liters per minute?
A) 270
B) 288
C) 300
D) 400
E) 405
Pumps A, B, and C pump water at their respective constant rates. Working simultaneously, A and B can fill an empty pool in 6 hours. Working simultaneously, B and C can fill the empty pool in 5 hours. Working simultaneously, A and C can fill the empty pool in 4 hours. Working simultaneously, A, B, and C can fill the empty pool in approximately how many hours?
A) 1.2
B) 1.6
C) 2.4
D) 3.2
E) 7.5
Each of two pumps delivers water into a tank at a constant rate of 30 liters per minute, and a third pump removes water from the tank at a constant rate of 15 liters per minute. If the three pumps start working simultaneously when the tank is filled to half of its capacity and continue working until the tank is full, it will take 12 minutes to fill the tank. What is the capacity, in liters, of the tank?
A) 1,080
B) 1,040
C) 960
D) 720
E) 540
Answer (2)
Let's address the problem step-by-step:
The setup involves two machines, A and B, assembling metal clips. Machine A can assemble 3,000 clips in 15 hours, and Machine B can assemble 3,000 clips in 12 hours. We need to figure out how many clips they assembled when working together, the impact of a modification, and how that affects their output.
Step 1: Determine Individual Rates of A and B
Machine A's rate of work is 15 3 , 000 = 200 clips per hour. Machine B's rate of work is 12 3 , 000 = 250 clips per hour.
Step 2: Combined Rate of Machines A and B
Working together, their combined rate is: 200 + 250 = 450 clips per hour.
In x hours, they assemble: 450 x clips.
Step 3: Impact of Modification on Machine A
After modification, Machine A's rate decreases by 25%. The new rate of A is: 200 × ( 1 − 0.25 ) = 150 clips per hour.
Machine B's rate stays the same at 250 clips per hour.
Step 4: New Combined Rate After Modification
The new combined rate is: 150 + 250 = 400 clips per hour.
In x hours after modification, they assemble: 400 x clips.
Step 5: Percentage Decrease in Total Clips Assembled
The decrease in the number of clips is: 450 x − 400 x = 50 x clips.
To find the percentage decrease relative to the original number of clips, use the formula: Percentage Decrease = ( 450 x 50 x ) × 100%
Simplifying, we get: 450 50 × 100 = 9 1 × 100 ≈ 11.11%
Thus, the total number of clips assembled after the modification is approximately 11% less than it was the day before.
Answer for this problem is option B: 11%.
After calculating the assembly rates of machines A and B, we found that the total clips assembled decreased by approximately 11% after a modification to machine A's rate. The final answer is option B) 11%.
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