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

2. Work = Rate Time Rate = Work Time Time = Work Rate
Work Problems
Work = Rate Time
Rate = Work
Time
Time = Work
Rate
Work = 1 (entire job)

3. 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?

4. 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.

5. Work Problems Rate = Work Time
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:

6. 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:

7. Work Problems John and Ana would take 18 minutes to mow the lawn
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.

8. 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?

9. 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.

10. Work Problems Joe’s Rate: Nancy’s Rate:
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:

11. Work Problems Amount of work completed by Nancy in 30 minutes:
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:

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

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

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

15. 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.

16. 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?

17. 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.

18. 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

19. 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:

20. 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:

21. Upstream-Downstream Problems

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