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?
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in - out = whats left
its best to define the rates in terms of a single time frame, such as a minute
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?
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pfft, my second ine IS the drain, can you do the other faucet?
@amistre64 so, \[1/15 + 1/25 = 1\]
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
* when 2 taps are open
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
1/15 + 1/12 - 1/25 takes care of the ins and outs
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
13b/300a = 1
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