Two pipes A and B jointly fill a reservoir in 4 hours. Operating independently, B would require 6 additional hours compared to A to fill the container. How much time does pipe A need to fill the reservoir on its own?
Show answer Hide answer
Answer: C. 6 hrs
Explanation
Letting pipe A take x hours means pipe B takes x plus six hours to fill the reservoir. Setting up a combined work rate equation equals one fourth based on their joint operating time. Solving the resulting quadratic equation yields an operating time of six hours for pipe A. Joint work problems combine individual operating rates by adding their fractional reciprocals. Quadratic equations arising from work word problems can be solved by factoring or formula. Time variables in physical problems must always yield positive real number solutions.
Construction project scheduling uses combined rate models to estimate crew completion times. Manufacturing assembly lines evaluate individual machine speeds to optimize joint production output. Engineering problem solving applies algebraic modeling to physical system performance. Option A suggests one hour which is too fast to produce the combined four hour duration. Option B proposes two hours which fails to satisfy the quadratic work rate equation. Option D offers eight hours which overestimates the time required for pipe A alone.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Two valves A and B fill a reservoir in 15 min and 20 min respectively. Opening both valves together, valve A is closed after 4 min. What total duration is necessary to fill the basin?
Show answer Hide answer
Answer: D. 14 min 40 sec
Valves A and B fill at individual rates of one-fifteenth and one-twentieth of the basin per minute. Working together for four minutes, both valves fill a total fraction of seven-fifteenths of the reservoir. The remaining...
Q2. Two pipes A and B fill a water reservoir in 4 and 5 hours respectively. Operating them sequentially for one hour each on an alternating basis, what duration is required to fill the container?
Show answer Hide answer
Answer: B. 4 hrs 24 min
Pipe A fills one quarter of the tank every single hour. Pipe B fills one fifth of the tank during its operating hour. Alternating operation fills nine twentieths of the tank every two hours. Work rates of individual pipe...
Q3. Two quantities X and Y trail a third quantity Z by 20% and 28% respectively. By what percentage does quantity Y fall short of quantity X?
Show answer Hide answer
Answer: C. 10%
Letting the third reference quantity Z be one hundred, quantity X equals eighty and quantity Y equals seventy two. The absolute difference between quantity X and quantity Y is eight units based on these established value...
Q4. Two pipes A and B fill a water reservoir in 2 minutes and 15 minutes respectively when operated separately. Both open together, but pipe A is closed 4 minutes post-commencement. How long will filling the reservoir take?
Show answer Hide answer
Answer: B. 10 min
Calculating individual filling rates gives one-twelfth and one-fifteenth of the reservoir per minute. Running both pipes together for the initial four minutes before closing pipe A fills a specific initial fraction. Allo...
Q5. Two pipes A and B can independently fill a container in 12 and 15 minutes respectively. A third pipe C discharges 45 liters of water every minute. Operating all pipes together fills the container in 15 minutes. What is the total water capacity of the container?
Show answer Hide answer
Answer: B. 540 liters
The combined net filling rate of all pipes over fifteen minutes equals the total tank volume. Pipe C extracts forty five liters per minute, influencing the overall net accumulation speed. Solving the algebraic equation f...
Q6. Two valves A and B fill a reservoir in 37 1/2 minutes and 45 minutes respectively. Opening both valves, the reservoir achieves full capacity in exactly half an hour provided valve B is closed after how long?
Show answer Hide answer
Answer: B. 9 min
Valve A runs for the entire duration of thirty minutes, filling four fifths of the total tank capacity. The remaining one fifth of the tank capacity must be filled by valve B before it is closed. Valve B fills this remai...