Math

QuestionA shower uses water at a constant rate. If it uses 2 gallons per minute, find the total gallons for any length of shower.

Studdy Solution

STEP 1

Assumptions1. The shower uses the same amount of water each minute it is on. . The relationship between shower length and gallons of water used is linear and directly proportional.

STEP 2

The constant of proportionality in a direct proportion is the value that relates the two quantities. In this case, it is the amount of water used per minute.
We can find the constant of proportionality by dividing the total amount of water used by the total shower length.
Constantofproportionality=TotalwaterusedTotalshowerlengthConstant\, of\, proportionality = \frac{Total\, water\, used}{Total\, shower\, length}

STEP 3

The unit rate is the amount of water used per minute. This is the same as the constant of proportionality in this case.
Unitrate=ConstantofproportionalityUnit\, rate = Constant\, of\, proportionality

STEP 4

To figure out how many gallons of water are used for any shower length, we can multiply the shower length by the unit rate (or the constant of proportionality).
Waterused=ShowerlengthtimesUnitrateWater\, used = Shower\, length \\times Unit\, rateNote The actual values for the total water used, total shower length, and shower length are not provided in the problem, so we cannot perform the actual calculations. However, the steps provided above outline the process to solve the problem.

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