For a certain bathtub it takes the hot water faucet 3 times

For a certain bathtub, it takes the hot water faucet 3 times as long to fill the tub as it does the cold water faucet. Left on together, the two faucets take 6 minutes to fill the tub. How long will it take the hot water faucet to fill the tub by itself? Do not do any rounding.

Solution

let the time required by cold water faucet be \"t\"

rime required by hot water faucet be \"3t\"               // since it takes 3 times as long to fill the tub as it does the cold water

when bpth are open they can fill in 6 minutes

therefore

1/T_both   = 1/T_hot   + 1/T_cold

1/6 = 1/3t +1/t

1/6 = 1/3t +3/3t               // multiplied and divided 1/t by \"3\"

1/6 = (1+3)/3t                   // denominator is same we can add the numbers

1/6 = 4/3t

multiply both sides by \"3t\"

3t/6 = 4*3t/3t

t/2=4

t = 8 minutes

time required by cold water faucet = 8 minutes

time required by hot water faucet = 3*t = 24 minutes