The depth of the water in Jeanne's hot tub varies directly with the number of minutes that the faucet is turned on. At 8.15 A.M Jeanne's started filling her circular hot tub with water. At 8.59 A.M there was a foot of water in the tub. When will the hot tub have 2 3/4 feet of water in it?
A.11:15 A.M
B.10:59 A.M
C.10.15 A.M
D.10:16 A.M
Can someone explain to me how to solve.
To raise the water level 1 foot took 44 minutes
so to raise it 2.75 ft will take 44(2.75) or 121 minutes
or 2:01 hrs
since she started at 8:15
it will be 2 3/4 ft deep at 8:15 + 2:01 or at 10:16
Thank You
To solve this problem, we need to use the concept of direct variation. In direct variation, when two quantities are directly proportional, they have a constant ratio between them. In this case, the depth of the water in the hot tub is directly proportional to the number of minutes the faucet is turned on.
First, let's find the constant of proportionality. We know that at 8.15 A.M, the hot tub had 0 feet of water, and at 8.59 A.M, it had 1 foot of water. This means that in 44 minutes (8.59 A.M - 8.15 A.M), the depth of the water increased by 1 foot. Therefore, the constant of proportionality is 1 foot per 44 minutes.
Next, we can set up a proportion to find the number of minutes it takes to reach 2 3/4 feet of water. Let's call the unknown number of minutes "x". The proportion would be:
(1 foot) / (44 minutes) = (2 3/4 feet) / (x minutes)
We can cross-multiply and solve for x:
1 * x = (44 minutes) * (2 3/4 feet)
x = (44/1) * (11/4) minutes
x = 121 minutes
Now, we need to determine the time when there will be 2 3/4 feet of water in the tub. Since Jeanne started filling her hot tub at 8.15 A.M, we can add 121 minutes (the time it takes to reach 2 3/4 feet) to get the answer.
8.15 A.M + 121 minutes = 10.16 A.M
Therefore, the correct answer is option D: 10:16 A.M.