<h1 class="subject">How many mintues does it take if both faucets are used?</h1>

The hot water faucet takes four minutes to fill a tub, and a cold-water faucet takes three minutes fo the same job. How long to fill the tub if both faucets are used?

use the idea that

time/ work rate = (1) job

for instance,,,,,the hot water takes 4 min to fill a tub

1/4 * time = 1 job

in one hour...1 * 1/4 --> 1/4 full

in 4 hours...4 * 1/4 --> 1 tubfull

therefore the formula would look something like this

t/4 + t/3 = 1

mult by lcd

3t + 4t = 12

t = 12/7

t= 1/ 5/7 min

Let x = the time it takes to fill the tub, then

x/4 + x/3 = 1

7x = 12

x = 12/7 minutes

timetaken if both faucets are used=1/[1/4+1/3]

=1/(7/12)

=12/7

=1 5/7 min

Assume the tub holds 120 gallons. The hot water tap flows at 30 gallons per minute, the cold at 40 gallons per minute.

Assuming the pipes leading to the faucets do not impose any restrictions, using both should flow at 70 gallons per minute.

70 gallons per minute will take just under 1 minute 43 seconds.

Hot water faucet = 1/4 of tub per minute

Cold water faucet = 1/3 of tub per minute

Hot + cold = 7/12 of tub per minute

Hot + cold will take 12/7 minutes = 1.714286 minutes = about 1 min 43 s