Write an equation for each and solve. A hot water faucet can fill a sink in 8 min while it takes

Write an equation for each and solve. A hot water faucet can...

Key Concepts

Work Rate Problems

These problems involve determining how much of a task can be completed per unit time by one or more agents. They focus on the relationship between an agent’s rate of work (such as filling a sink per minute) and the time taken to complete the entire task.

Unit Rate Calculation

This concept involves converting the total time required to complete a task into a unit rate (for example, the fraction of the task completed in one minute). It is done by taking the reciprocal of the total time, which is essential for comparing and combining the contributions of different agents.

Combined Work Equations

When multiple agents work together, their individual work rates are added to obtain a total combined rate. This sum reflects the portion of the job completed per unit time when all agents operate simultaneously, forming the basis for setting up and solving the related equation.

Reciprocal Relationship in Work Problems

The time taken to complete a task is the reciprocal of the work rate. Once the combined work rate is known, taking its reciprocal gives the overall time required to complete the task, highlighting the inverse relationship between rate and time.

Transcript

00:01 In this scenario, we're given that a hot water takes eight minutes to fill a sink completely, and the cold water faucet takes six minutes to fill the same same completely.

00:09 And we want to figure out if both of them were running simultaneously, how long would it take to fill up the water, to fill up the sink.

00:16 So for this kind of problem, we want to figure out what the rates are for each of the two faucets.

00:20 So the rate, right in this case, is equal to, is equal to one job per out, one hour.

00:33 So basically how much, when we figure out how much of the sink it can fill, how much the job is done after one hour, we can figure out the rate for each, and supplies to each faucet.

00:43 So for example, for the hot water faucet, we have one job completed in eight hours, eight minutes.

00:52 So in this case, this would be minute and one minute.

01:05 And, but we keep in mind that we, what we want is we want to figure out how long it takes for how much of the job is completed in one minute.

01:17 So we set this as x.

01:18 And we see that when we cross multiply this proportion here, we get 8x is equal to 1.

01:28 And x is equal to 1 divided by 8.

01:31 So 1 8th.

01:32 So the rate for hot water is 1 eighth job per minutes.

01:38 And we can do the same thing for cold water.

01:40 Cold water gets one job done in six minutes.

01:47 But just like with a hot water faucet, we want to figure out how much of the job it can complete in one minute...

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