Taps A, B, and C fill a tank in 12, 15, and 20 hours. With A running constantly and B and C alternating hourly, when will the tank be full_________?
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Answer: C. 7 hours
Explanation
Tap A fills one-twelfth of the tank per hour, while taps B and C fill one-fifteenth and one-twentieth per hour respectively. Running tap A constantly while alternating B and C hourly creates a repeating two-hour filling cycle with consistent volumetric progress. Summing the hourly fractional contributions over successive cycles reveals that the tank fills completely in exactly seven hours. Pipe and cistern problems calculate work rates by determining the fraction of a tank filled by each tap per unit of time. Alternating work schedules require tracking cumulative progress cycle by cycle until the total target volume is achieved. Fractions with different denominators must be converted to common denominators before adding or subtracting them.
Option A suggests six hours, which is insufficient time to complete the filling process given the alternating taps. Option B proposes six and two-thirds hours, missing the exact cycle completion point required to fill the tank. Option D offers seven and one-half hours, overestimating the total duration needed to reach maximum capacity.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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