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stupidinmath Group Title

A cold water faucet could fill the sink in 15 minutes and a hot water faucet can fill it in 12 minutes. the drain can empty the sick in 25 minutes. if both faucets are open and the drain is open, how long will it take to fill the sink?

  • 2 years ago
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  1. amistre64 Group Title
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    in - out = whats left

    • 2 years ago
  2. amistre64 Group Title
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    its best to define the rates in terms of a single time frame, such as a minute

    • 2 years ago
  3. amistre64 Group Title
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    15 minutes = 1 sink full; divide each side by 15 1 minute = 1/15 of a sink full and for the other one 25 minutes = 1 sink full; divide each side by 25 1 minute = 1/25 of a sink full so the total amount in is 1/15 + 1/25 each minute; can you determine the amount that is drained per minute?

    • 2 years ago
  4. amistre64 Group Title
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    pfft, my second ine IS the drain, can you do the other faucet?

    • 2 years ago
  5. stupidinmath Group Title
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    @amistre64 so, \[1/15 + 1/25 = 1\]

    • 2 years ago
  6. stupidinmath Group Title
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    ?

    • 2 years ago
  7. cwrw238 Group Title
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    following from what amistre said, if t = time to fill the tank when drain is closed nd t20 taps are open then 1/15 + 1/12 = 1/t solve for t

    • 2 years ago
  8. cwrw238 Group Title
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    * when 2 taps are open

    • 2 years ago
  9. amistre64 Group Title
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    almost, but first we need to determine how much "work" is done in a normalized time frame. Hot + Cold - Drain = Amount left to play with

    • 2 years ago
  10. amistre64 Group Title
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    1/15 + 1/12 - 1/25 takes care of the ins and outs

    • 2 years ago
  11. amistre64 Group Title
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    spose 1/15 + 1/12 - 1/25 = a/b this tells us that: a/b of the sink is filled in 1 minute; multiply each side by b/a to get 1 sink is filled in b/a minutes

    • 2 years ago
  12. stupidinmath Group Title
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    13b/300a = 1

    • 2 years ago
  13. amistre64 Group Title
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    1/15 + 1/12 - 1/25 = 11/100 so, 11/100 of the the sink fills in 1 minute; multiply each side by 100/11 to determine the number of minutes it takes to fill 1 sinnk 11/100 sink : 1 minute 1 sink : 100/11 minutes

    • 2 years ago
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