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Solving Rational Equations: Applications in Work and Motion, Exercises of Algebra

Step-by-step instructions on how to set up and solve application problems using rational equations. The examples cover work problems, motion problems, and negative work. Students will learn how to assign variables, write equations, and solve for time or rate.

Typology: Exercises

2012/2013

Uploaded on 01/07/2013

tahir
tahir 🇮🇳

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Chapter 6.5: Applications of Rational
Equations
Objectives:
Set up and solve work problems
Set up and solve motion problems
Distance =(Rate)x(Time)
Steps for Solving Application Problems:
1. Read, understand the question
2. Assign a variable (What is it asking
for?)
3. Write an equation
4. Solve the equation
5. Check, does it make sense?
Work Formula:
job 1 together) takes(time
ngperson/thi 2nd takestime
1
together) takes(time
ngperson/thi1st takestime
1
Solving For Time It Takes To Do a Task Together
Ex: One person can do a task in 6 hours. Another can do the same task in 4 hours. How long will
it take them to do the task together?
Let ______ = __________________________
Equation:
  job 1 togetherit takes timengperson/thi 2nd it takes over time 1 togetherit take s timengpe rson/thi1st it takes over time 1
_____________________________________________________
Answer: They can do the task together in 2.4 hours.
Solving For Time It Takes a Person/Thing To Do a Task Alone
Ex: Say you and a friend can do a task in 12 hours. You can do the same task by yourself in 18
hours. How long would it take your friend to do the task alone?
Let ______ = __________________________
Equation:
  job 1 togetherit takes timengperson/thi 2nd it takes over time 1 togetherit take s timengpe rson/thi1st it takes over time 1
_____________________________________________________
Answer: It would take your friend 36 hours to do the task alone.
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Chapter 6.5: Applications of Rational

Equations

Objectives: Set up and solve work problems Set up and solve motion problems Distance =(Rate)x(Time)

Steps for Solving Application Problems:

  1. Read, understand the question
  2. Assign a variable (What is it asking for?)
  3. Write an equation
  4. Solve the equation
  5. Check, does it make sense?

Work Formula:

(timetakestogether) 1 job timetakes2ndperson/thing

1 (timetakestogether) timetakes1stperson/thing

1

Solving For Time It Takes To Do a Task Together

Ex: One person can do a task in 6 hours. Another can do the same task in 4 hours. How long will it take them to do the task together?

Let ______ = __________________________

Equation:

1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job

_____________ __________ _____________ __________ _______

Answer: They can do the task together in 2.4 hours.

Solving For Time It Takes a Person/Thing To Do a Task Alone

Ex: Say you and a friend can do a task in 12 hours. You can do the same task by yourself in 18 hours. How long would it take your friend to do the task alone?

Let ______ = __________________________

Equation:

1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job

_____________ __________ _____________ __________ _______

Answer: It would take your friend 36 hours to do the task alone.

Solving Problems Involving Negative Work

Ex: Say a pipe can fill a tank in 4 hours, and another pipe can empty the tank in 6 hours. If both pipes are working, how long will it take to fill the tank?

Let ______ = __________________________

Equation:

1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job

_____________ __________ _____________ __________ _______

Answer: It takes 12 hours to fill the tank while both pipes are working.

Ex: While one pipe is pumping water in and another is pumping water out, a tank can be filled 75 minutes. If the pipe that pumps water out was only working, the tank could be emptied in 50 minutes. If the pipe that pumps water in was only working, how long would it take to fill the tank?

Let ______ = __________________________

Equation:

1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job

_____________ __________ _____________ __________ _______

Answer: It would take 30 minutes to fill the tank if the pipe that pumps water in was only working.

Ex: Say a dude rides a bike on a trail part of the time at 6 mph and part of the time at 10 mph. If the total distance traveled was 28 miles in 4 hours, how long did the dude ride at each speed?

Let ______ = __________________________ Then _________ = _____________________________

Rate Distance rate

dist time

1 st^ Part of the trail

2 nd^ Part of the trail

total

Equation:

          timeit tookfor the1stpart timeit tookfor the2ndpart totaltimeit took

_____________ _____________ __________ ___

Answer: The dude rode 6 mph for 3 hours, and 10 mph for 1hour.

Ex: Say you and a friend started off on a trail at the same time, but you went 9 mph, and your friend went 6 mph. Since you went faster, you finished the trail 0.25 hours before your friend. Determine the length of the trail.

Let ______ = __________________________

Rate Distance rate

dist time

You

Your friend

Equation:

Answer: The trail is 4.5 miles long.