Question 77429
Let x=time to fill the sink if both faucets are left on

Cold water faucet fills sink at the rate of 1/10 of the sink per min

Hot water faucet fills sink at the rate of 1/12 of the sink per min

Both together fill sink at the rate of 1/10+1/12 of the sink per min (The LCM is 60)

1/10=6/60
1/12=5/60-------So:

Both together fills sink at the rate of 6/60+5/60=11/60 of the sink per minute

Now the question is:  If both together can fill the sink at the rate of 11/60 of the sink per min, how long will it take for both together to fill 60/60 (all) of the sink????  Our equation to solve is:

(11/60)(x)=60/60  multiply both sides by 60 to get rid of the fractions

11x=60  divide both sides by 11

x=5.4545 minutes--------------time for both together to fill tank

CK
Cold water faucet rate * minutes+Hot water faucet rate * minutes must equal 1 (full tank)
5.4545(1/10)+5.4545(1/12)=1
0.54545+0.45454=1
0.99999=1---------------------close enough


Hope this helps-------------------ptaylor