## stupidinmath 2 years ago 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?

1. amistre64

in - out = whats left

2. amistre64

its best to define the rates in terms of a single time frame, such as a minute

3. amistre64

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?

4. amistre64

pfft, my second ine IS the drain, can you do the other faucet?

5. stupidinmath

@amistre64 so, \[1/15 + 1/25 = 1\]

6. stupidinmath

?

7. cwrw238

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

8. cwrw238

* when 2 taps are open

9. amistre64

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

10. amistre64

1/15 + 1/12 - 1/25 takes care of the ins and outs

11. amistre64

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

12. stupidinmath

13b/300a = 1

13. amistre64

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