Question 1197891
rate * time = quantity
quantity = 1 full tub.
for the cold water faucet, the equation becomes:
rate * 8 = 1
solve for rate to get rate = 1/8.
for the hot water faucet, the equation becomes:
rate * 12 = 1
solve for rate to get rate = 1/12.
when they are both working together, their rates are additive.
you get (1/8 + 1/12) * time = 1
1/8 * 3/3 = 3/24
1/12 * 2/2 = 2/24
formula becomes:
(3/24 + 2/24) * time = 1 which becomes:
5/24 * time = 1
solve for time to get:
time = 1*24/5 = 24/5 minutes.
that's how long to fill the tub when both faucets are open.
the cold water faucet will fill 1/8 * 24/5 = 3/5 of the tub in 24/5 minutes.
the hot water faucet will fill 1/12 * 24/5 = 2/5 of the tub in 24/5 minutes.
3/5 + 2/5 = 5/5 = 1 = the whole tub in the same 24/5 minutes.


your solution is that it will take 24/5 minutes to fill the tub if both faucets are open.
24/5 = 4.8 minutes in decimal format.