Pipes P, Q, and R fill a cistern in 20, 15, and 12 minutes respectively. How many minutes will all three take combined:__________?
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Answer: A. 5 min
Explanation
Individual work rates for pipes P, Q, and R are one twentieth, one fifteenth, and one twelfth per minute. Summing the fractions one twentieth, one fifteenth, and one twelfth gives a combined rate of twelve over sixty. Simplifying twelve over sixty yields one fifth per minute, meaning all three pipes together take five minutes. Combined work rates in pipe problems are found by summing the individual reciprocal time rates. Fractions with different denominators must be converted to a common denominator before addition. The total time required to complete a task is the reciprocal of the combined work rate.
Civil engineers calculate simultaneous pipe discharge rates to prevent urban flooding during heavy rains. Pool maintenance technicians determine how fast multiple inlet hoses can fill a swimming pool. Industrial chemical processing plants coordinate multiple intake valves to fill reaction vats quickly. Option b overestimates the time by ignoring the additive nature of concurrent pipe flow rates. Option c corresponds to the slowest individual pipe filling time rather than the combined rate. Option d represents the rate of the slowest single pipe working alone without assistance.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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