Use units do help you answer the question. If necessary, round your answer to two decimal places.
Suppose water flows from a shower at a rate of 0.32 cubic feet per minute. Do you use more water bf taking a 12-minute shower or by filling a bathtub with 0.4 cubic yards of water and by how much?
To compare the amount of water used in a 12-minute shower to filling a bathtub with 0.4 cubic yards of water, we need to convert the units to be consistent.
1 cubic yard = 27 cubic feet
0.4 cubic yards = 0.4 * 27 cubic feet = 10.8 cubic feet
Now, let's calculate the amount of water used in a 12-minute shower:
Water flow rate = 0.32 cubic feet per minute
Water used in a 12-minute shower = 0.32 cubic feet/minute * 12 minutes = 3.84 cubic feet
Comparing this to filling the bathtub, 3.84 cubic feet of water used in a 12-minute shower is less than 10.8 cubic feet of water used to fill the bathtub. Therefore, you use more water by filling the bathtub. The difference in water usage is 10.8 cubic feet - 3.84 cubic feet = 6.96 cubic feet.
To determine which option uses more water, let's compare the total volume of water used in each scenario.
Given:
Shower flow rate = 0.32 cubic feet/minute
Shower duration = 12 minutes
First, let's calculate the total volume of water used during a 12-minute shower:
Volume of water used in shower = Flow rate x Time duration
= 0.32 cubic feet/minute x 12 minutes
= 3.84 cubic feet
Next, let's convert the volume of water used in the shower to cubic yards:
1 cubic yard = 27 cubic feet
Volume of water used in shower (cubic yards) = Volume of water used in shower (cubic feet) / 27
= 3.84 cubic feet / 27
= 0.1422 cubic yards (rounded to 2 decimal places)
Now, let's compare this with the volume of water used to fill the bathtub:
Volume of water used to fill bathtub = 0.4 cubic yards
Finally, we can determine the difference in water usage:
Difference = Volume of water used to fill bathtub - Volume of water used in shower
= 0.4 cubic yards - 0.1422 cubic yards
= 0.2578 cubic yards
Therefore, you would use more water by filling the bathtub with 0.4 cubic yards of water compared to taking a 12-minute shower. The difference in water usage is approximately 0.26 cubic yards.
To answer this question, we need to compare the amount of water used in each scenario: taking a 12-minute shower and filling a bathtub with 0.4 cubic yards of water.
First, let's convert the flow rate of the shower from cubic feet per minute to cubic yards per minute to match the units of the bathtub.
1 cubic yard is equal to 27 cubic feet.
So, the flow rate of the shower in cubic yards per minute can be calculated as:
0.32 cubic feet/min * (1 cubic yard / 27 cubic feet) = 0.01185 cubic yards/min
Now, let's calculate the amount of water used in the shower for 12 minutes:
0.01185 cubic yards/min * 12 minutes = 0.1422 cubic yards
Now, we can compare the amount of water used in the shower (0.1422 cubic yards) to the amount of water used for filling the bathtub (0.4 cubic yards).
By subtracting the amount of water used in the shower from the amount used for filling the bathtub, we can determine the difference:
0.4 cubic yards - 0.1422 cubic yards = 0.2578 cubic yards
Therefore, it takes approximately 0.2578 cubic yards more water to fill the bathtub compared to taking a 12-minute shower.