**Real World Problems** MA.912.A.5.7 Solve real-world problems involving rational equations (mixture, distance, work, interest, and ratio).

**Work Problems** Work = Rate Time Rate = Work Time Time = Work Rate Work = 1 (entire job)

**Work Problems** 1. John and Ana must mow the lawn before they can go swimming. Working alone, John would take 30 minutes and Ana would take 45 minutes. If they both work together how long would it take to do the job?

**Work Problems** 1. John and Ana must mow the lawn before they can go swimming. Working alone, John would take 30 minutes and Ana would take 45 minutes. If they both work together how long would it take to do the job? * Identify the question being asked and define the variable.

**Work Problems** 1. John and Ana must mow the lawn before they can go swimming. Working alone, John would take 30 minutes and Ana would take 45 minutes. If they both work together how long would it take to do the job? Rate = Work Time John’s Rate: Ana’s Rate:

**Work Problems** 1. John and Ana must mow the lawn before they can go swimming. Working alone, John would take 30 minutes and Ana would take 45 minutes. If they both work together how long would it take to do the job? Amount of work completed By Ana in x minutes: Amount of work completed By John in x minutes:

**Work Problems** 1. John and Ana must mow the lawn before they can go swimming. Working alone, John would take 30 minutes and Ana would take 45 minutes. If they both work together how long would it take to do the job? John and Ana would take 18 minutes to mow the lawn if they were to work together.

**Work Problems** 2. Nancy must mow the lawn before she can go to the movies. Working alone, she would take 50 minutes. Her friend Joe decides to help, and they complete the Job in 30 minutes. How long would it have taken Joe to mow the lawn on his own?

**Work Problems** 2. Nancy must mow the lawn before she can go to the movies. Working alone, she would take 50 min. Her friend Joe decides to help, and they complete the Job in 30 minutes. How long would it have taken Joe to mow the lawn on his own? * Identify the question being asked and define the variable.

**Work Problems** 2. Nancy must mow the lawn before she can go to the movies. Working alone, she would take 50 minutes. Her friend Joe decides to help, and they complete the Job in 30 minutes. How long would it have taken Joe to mow the lawn on his own? Joe’s Rate: Nancy’s Rate:

**Work Problems** 2. Nancy must mow the lawn before she can go to the movies. Working alone, she would take 50 minutes. Her friend Joe decides to help, and they complete the Job in 30 minutes. How long would it have taken Joe to mow the lawn on his own? Amount of work completed by Nancy in 30 minutes: Amount of work completed by Joe in 30 minutes:

**Work Problems** Amount of work completed by Nancy in 30 minutes: Amount of work completed by Joe in 30 minutes:

**Work Problems** Joe would take 75 minutes to mow the lawn on his own.

**Solving Real World Problems** Distance = Rate Time Rate = Distance Time (Average Speed) Time = Distance Rate

**Upstream-Downstream Problems** 3. Suppose you are traveling through the water at x km/h against a current of 5 km/h your avg speed (rate) would be ______, where x is your speed in still water. You want to complete a 10 km trip in 3 hours. Write an equation to solve for your avg speed.

**Upstream-Downstream Problems** 3. A boat moves through the water at x km/h. It makes a journey 20 km upstream against a current of 3 km/h and then returns with the current. How fast must the boat travel through the water in order to complete the trip in 5 hours?

**Upstream-Downstream Problems** 3. A boat moves through the water at x km/h. It makes a journey 20 km upstream against a current of 3 km/h and then returns with the current. How fast must the boat travel through the water in order to complete the trip in 5 hours? * Identify the question being asked and define the variable.

**Upstream-Downstream Problems** 3. A boat moves through the water at x km/h. It makes a journey 20 km upstream against a current of 3 km/h and then returns with the current. How fast must the boat travel through the water in order to complete the trip in 5 hours? Net Speed Upstream: against the current Net Speed Downstream: with the current

**Upstream-Downstream Problems** 3. A boat moves through the water at x km/h. It makes a journey 20 km upstream against a current of 3 km/h and then returns with the current. How fast must the boat travel through the water in order to complete the trip in 5 hours? Number of Hours Upstream: Number of Hours Downstream:

**Upstream-Downstream Problems** 3. A boat moves through the water at x km/h. It makes a journey 20 km upstream against a current of 3 km/h and then returns with the current. How fast must the boat travel through the water in order to complete the trip in 5 hours? Total time for round trip:

**Upstream-Downstream Problems**

**Upstream-Downstream Problems** The boat must travel at a rate of 9 km/h