Problema Solution
For a certain bathtub, the hot water faucet can fill the tub in minutes. The cold water faucet can fill the tub in minutes. If both faucets are used together, how long will it take to fill the tub?
Answer provided by our tutors
Let
t1 = time (in minutes) needed to fill the tub with hot water faucet open
t1 = time (in minutes) needed to fill the tub with cold water faucet open
t = time to fill the tub with both faucets open
We want to find t using t1 and t2.
1/t1 + 1/t2 = 1/t multiply both sides by t
t/t1 + t/t2 = 1
t (1/t1 + 1/t2) = 1
t (t1 + t2)/ t1*t2 = 1
t = t1*t2 / (t1 + t2) minutes
If both faucets are used together it takes t1*t2 / (t1 + t2) minutes to fill the tub.