SOLUTION: If the cold-water faucetis left on, the sink will fill in 10 min. If the hot-water faucetis left on, the sink will fill in 12 min. How long would it take the sink to fill if both f
Algebra ->
Rate-of-work-word-problems
-> SOLUTION: If the cold-water faucetis left on, the sink will fill in 10 min. If the hot-water faucetis left on, the sink will fill in 12 min. How long would it take the sink to fill if both f
Log On
Question 77429This question is from textbook beginning algebra
: If the cold-water faucetis left on, the sink will fill in 10 min. If the hot-water faucetis left on, the sink will fill in 12 min. How long would it take the sink to fill if both faucetes are left on? This question is from textbook beginning algebra
You can put this solution on YOUR website! 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
