QuestionA hose fills a hot tub at 2.16 gallons/min. How many hours to fill a 261-gallon tub? It will take $\square$ hours.

Studdy Solution

STEP 1

Assumptions1. The rate at which the hose fills the hot tub is.16 gallons per minute. . The total volume of the hot tub is261 gallons.
3. The hose fills the hot tub at a constant rate.

STEP 2

First, we need to find the total time it takes to fill the hot tub. We can do this by dividing the total volume of the hot tub by the rate at which the hose fills the hot tub.
$Time\, (in\, minutes) = \frac{Total\, volume}{Rate}$

STEP 3

Now, plug in the given values for the total volume and the rate to calculate the time in minutes.
$Time\, (in\, minutes) = \frac{261\, gallons}{2.16\, gallons/minute}$

STEP 4

Calculate the time in minutes.
$Time\, (in\, minutes) = \frac{261}{2.16} \approx120.83\, minutes$

STEP 5

Now that we have the time in minutes, we need to convert this to hours since the problem asks for the time in hours. We can do this by dividing the time in minutes by the number of minutes in an hour (60).
$Time\, (in\, hours) = \frac{Time\, (in\, minutes)}{60}$

STEP 6

Plug in the value for the time in minutes to calculate the time in hours.
$Time\, (in\, hours) = \frac{120.83\, minutes}{60}$

STEP 7

Calculate the time in hours.
$Time\, (in\, hours) = \frac{120.83}{60} \approx2.01\, hours$ It will take approximately2.01 hours to fill the hot tub.

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