Question 1085718
<font color="black" face="times" size="3">Table
<table border=1 cellpadding=3><tr><th></th><th>Time</th><th>Rate</th></tr><tr><td>Tap A</td><td>15</td><td>1/15</td></tr><tr><td>Tap B</td><td>20</td><td>1/20</td></tr><tr><td>Total</td><td></td><td>7/60</td></tr></table>
The table represents the rates and times for both taps. 


The time values are in minutes. The rates are in jobs per minute


A rate like "1/20" means tap B can get 1/20th of a job done per minute. Each minute, tap B fills up 1/20 = 0.05 = 5% of the sink. 


The combined rate of 7/60 is the result of adding the fractions 1/15 and 1/20 like so
(1/15) + (1/20) = (4/4)*(1/15) + (3/3)*(1/20)
(1/15) + (1/20) = 4/60 + 3/60
(1/15) + (1/20) = (4+3)/60
(1/15) + (1/20) = 7/60


This means that if the taps are opened together, then the sink is filled at a rate of 7/60 jobs per minute. Put another way, the two taps work together to fill the sink 7/60 of the way for each minute.


Let t be the time it takes for both sinks to get the job done together. In this case,
(combined rate)*(time) = 1
where "1" represents the fact that 1 job is completed, ie the sink is full 100%


The combined rate found earlier is 7/60. The time is unknown. Let's solve for t
(combined rate)*(time) = 1
(7/60)*(t) = 1
60*(7/60)*(t) = 60*1
7*t = 60
7*t/7 = 60/7
t = 60/7 <font color=red><--- Exact answer as a fraction</font>
t = 8.571429 <font color=red><--- Approximate answer in decimal form</font>


It takes roughly 8.571429 minutes for the two taps to completely fill the sink. This is assuming that one tap doesn't hinder the other in any way.</font>