Applications of Rational Equations (Motion & Work Problems)

Applications of Rational Equations (Motion & Work Problems)

Lesson Goals

• Review on Solving Rational Equations

• Review on Solving Number Problem

• Examples on Solving Motion and Work Problem

• Solving Motion and Number Problem

• Reminders

FA 1.18 REVIEW

Solving Radical Equations and Number Problem

(1 pt each for solving rational eq., 2 pts each for word problems)

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1) Solve:

 $3+\frac{y}{y-4}=\frac{4}{y-4}$  

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2) Solve:

 $\frac{12}{a^2-4}=\frac{3}{a-2}-1$  .

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3) Solve.

 $\frac{2}{v-1}=\frac{5}{v+3}$  .

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4) Solve:

 $\frac{6x+22}{x^2-2x-24}=\frac{x-3}{x+4}+\frac{x+2}{x-6}$  .

Multiple Choice

5) Solve for b.

 $\frac{2}{a}=\frac{3}{b}-\frac{1}{ab}$  .

•  $b=3a-1$  

•  $b=\frac{3a-1}{2}$  

•  $b=\frac{2a-1}{3}$  

•  $b=\frac{2a+1}{3}$  

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6) Find two consecutive integers such that the sum of one-third of the first and one-fourth of the second is 9.

(Separate your answers with a comma, no space in between)

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7) If the numerator of

 $\frac{19}{6}$  is increased by a certain number and if the value of the denominator is doubled, the result is 3. Find the number.

Solutions will be posted in the Help Center channel.

SOLVING MOTION AND WORK WORD PROBLEMS

a) Motion Problem 1

distance $=rate\cdot time$ 
time $=\frac{d}{r}$  

continuation...

b) Motion Problem 2

upstream = direction opposite in which the river flows (lesser speed)

downstream = direction in which a river flows (greater speed)

c) Work Problem 1

continuation

d) Work Problem 2

another method of solving

e) Work Problem 3

FA 1.19 Solving Motion and Work Word Problems

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1) An airplane travels 1 260 km in the same time a car travels 420 km. If the rate of the car is 20 kph less than the rate of the airplane, find the rate of each.​

(separate your answers with a comma, don't put space in between and don't forget to put the unit per answer. Example: 2kph,3kph)

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2) Julius can paint a house three times faster than Ruben. Working together, they can paint a house in 4 days. How long would it take the faster painter if he works alone?

Sample answer: 2 1/2 days (put space in between the whole number and fraction -- use mixed fraction)

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3) To do a job alone, it will take Shawn 3 days, Mona 4 days, and Harriet 7 days. How long will it take if they work together to complete the job?

(use improper fraction)

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4) Suppose a swimming pool has two intake pipes. One pipe fills the pool in 10 hours and the other in 15 hours. If both pipes are open, how long will it take to fill the pool?

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5) The speed of the current is 3 kph. A boat travels 4 km upstream in the same time it takes to travel 10 km downstream. What is the speed of the boat in still water?

Next meeting you will answer a Reinforcement Activity in desmos.