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It takes 5 minutes to fill the sink using only the cold water. If both the hot water and the cold water are turned on, it takes 2 minutes to fill the sink. Which is the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water?

A table showing Rate in part per minute, Time in minutes, and Part of Sink Filled. The first row shows Cold and has 5, 2, and 10. The second row shows Hot, and has x, 2, and 2 x.
A table showing Rate in part per minute, Time in minutes, and Part of Sink Filled. The first row shows Cold and has 2, 5, and 10. The second row shows Hot, and has x, 5, and 5 x.
A table showing Rate in part per minute, Time in minutes, and Part of Sink Filled. The first row shows Cold and has StartFraction 1 Over 5 EndFraction, 2, and StartFraction 2 Over 5 EndFraction. The second row shows Hot, and has StartFraction 1 Over x EndFraction, 2, and StartFraction 2 Over x EndFraction
A table showing Rate in part per minute, Time in minutes, and Part of Sink Filled. The first row shows Cold and has StartFraction 1 Over 2 EndFraction, 5, and StartFraction 5 Over 2 EndFraction. The second row shows Hot, and has StartFraction 1 Over x EndFraction, 5, and StartFraction 5 Over x EndFraction

1 Answer

2 votes

Answer:

Hot water: 3 units of work per 10 minutes

Explanation:

To determine the time it takes to fill the sink using only the hot water, we can use the concept of work rate. The work rate is the amount of work done per unit of time.

Let's assume that filling the sink using only the cold water is considered one unit of work. We know that it takes 5 minutes to complete this work. So, the work rate for filling the sink with only cold water is 1 unit of work per 5 minutes.

When both the hot water and the cold water are turned on, the work rate increases. Now it takes only 2 minutes to complete the same unit of work. So, the combined work rate for filling the sink with both hot and cold water is 1 unit of work per 2 minutes.

To find the work rate of only the hot water, we need to subtract the work rate of the cold water from the combined work rate. The difference in work rates represents the work done by the hot water alone.

From the given information, the table that represents the work rates can be constructed as follows:

Cold water: 1 unit of work per 5 minutes

Combined (Hot + Cold) water: 1 unit of work per 2 minutes

To find the work rate of only the hot water:

Combined work rate - Cold water work rate = Hot water work rate

1 unit of work per 2 minutes - 1 unit of work per 5 minutes = x unit of work per ? minutes

Simplifying the equation:

1/2 - 1/5 = x/?

To find x, we can find the least common multiple (LCM) of the denominators (2 and 5), which is 10. Then, multiply the numerators and divide by the denominators:

(5/10) - (2/10) = x/10

(3/10) = x/10

Therefore, the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water, is:

Hot water: 3 units of work per 10 minutes

To determine the time it takes to fill the sink using only the hot water, we can use the concept of work rate. The work rate is the amount of work done per unit of time.

Let's assume that filling the sink using only the cold water is considered one unit of work. We know that it takes 5 minutes to complete this work. So, the work rate for filling the sink with only cold water is 1 unit of work per 5 minutes.

When both the hot water and the cold water are turned on, the work rate increases. Now it takes only 2 minutes to complete the same unit of work. So, the combined work rate for filling the sink with both hot and cold water is 1 unit of work per 2 minutes.

To find the work rate of only the hot water, we need to subtract the work rate of the cold water from the combined work rate. The difference in work rates represents the work done by the hot water alone.

From the given information, the table that represents the work rates can be constructed as follows:

Cold water: 1 unit of work per 5 minutes

Combined (Hot + Cold) water: 1 unit of work per 2 minutes

To find the work rate of only the hot water:

Combined work rate - Cold water work rate = Hot water work rate

1 unit of work per 2 minutes - 1 unit of work per 5 minutes = x unit of work per ? minutes

Simplifying the equation:

1/2 - 1/5 = x/?

To find x, we can find the least common multiple (LCM) of the denominators (2 and 5), which is 10. Then, multiply the numerators and divide by the denominators:

(5/10) - (2/10) = x/10

(3/10) = x/10

Therefore, the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water, is:

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