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Rational Expressions Chapter 10 Distance – Rate - Time QQQQ TTTT WWWW HHHH.

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Presentation on theme: "Rational Expressions Chapter 10 Distance – Rate - Time QQQQ TTTT WWWW HHHH."— Presentation transcript:

1 Rational Expressions Chapter 10 Distance – Rate - Time QQQQ TTTT WWWW HHHH

2 Motion Problems Motion Problems Motion problems involve distance, time and rate. The equation that links these concepts is called The Distance Formula: d = r t d = distance t = time r = rate miles miles kilometers kilometers meters meters feet feet inches inches hours hours minutes minutes seconds seconds days days years years miles/hour miles/hour km/min. km/min. m/s m/s ft./sec. ft./sec. inches/sec. inches/sec.

3 Motion Problems Motion Problems Motion problems involve distance, time and rate. The equation that links these concepts is called The Distance Formula: d = r t d = distance t = time r = rate Youll need to be comfortable with using and manipulating the distance formula. miles/hour miles/hour km/min. km/min. m/s m/s ft./sec. ft./sec. inches/sec. inches/sec.

4 Rational Expressions Chapter 10 Distance – Rate - Time

5 Here is a strategy to solve motion problems Here is a strategy to solve motion problems 1. Read the problem (three times) picking out key information 2. Draw a diagram of what is happening. 3. Make a table that relates distance, rate and time. 5. Answer the question – include the units! Distance = rate x time 4. Use the table to write an equation.

6 Distance = rate x time Biker Walker 54 miles 18 miles x = speed of walker x + 8 = speed of cyclist Example 1 A bicyclist travels 8 miles per hour faster than a walker. The cyclist travels 54 miles in the same time it takes the walker to walk 18 miles. Find their speeds. A bicyclist travels 8 miles per hour faster than a walker. The cyclist travels 54 miles in the same time it takes the walker to walk 18 miles. Find their speeds.

7 Example 1 Time Walker Time Biker Distance = rate x time Biker Walker A bicyclist travels 8 miles per hour faster than a walker. The cyclist travels 54 miles in the same time it takes the walker to walk 18 miles. Find their speeds.

8 Example 1 A bicyclist travels 8 miles per hour faster than a walker. The cyclist travels 54 miles in the same time it takes the walker to walk 18 miles. Find their speeds.

9 # 2 One car travels 20 mph faster than the other car. While the faster car goes 240 miles the other car travels 180 miles. Find their speeds. Distance = rate x time 240 x + 20 x x = speed of red (slower) car 180 Slow car Fast car

10 # 2 One car travels 20 mph faster than the other car. While the faster car goes 240 miles the other car travels 180 miles. Find their speeds. Distance = rate x time x + 20 x x = speed of red (slower) car Time Slow Car Time Fast Car Slow car Fast car

11 # 2 One car travels 20 mph faster than the other car. While the faster car goes 240 miles the other car travels 180 miles. Find their speeds.

12 An airplane can fly at a speed of 240 m.p.h. in calm air. It takes the same time to fly 1080 miles with the wind as it does 840 miles against the wind. Find the speed of the wind. An airplane can fly at a speed of 240 m.p.h. in calm air. It takes the same time to fly 1080 miles with the wind as it does 840 miles against the wind. Find the speed of the wind. Example 3 Wind speed in calm air = 240 w = ? d = 1080 miles d = 840 miles

13 An airplane can fly at a speed of 240 m.p.h. in calm air. It takes the same time to fly 1080 miles with the wind as it does 840 miles against the wind. Find the speed of the wind. An airplane can fly at a speed of 240 m.p.h. in calm air. It takes the same time to fly 1080 miles with the wind as it does 840 miles against the wind. Find the speed of the wind. Example 3 Distance = rate x time With Against w w Let w = speed of wind Timewith wind Timeagainst wind

14 The speed of a freight train is 14 km/h slower than the speed of a passenger train. The freight train travels 330 km in the same time that it takes the passenger train to travel 400 km. Find the speed of each train. One car travels 40 km/h faster than another. While one travels 150 km, the other goes 350 km. Find their speeds. A lab tested two high-speed trains. One travels 40 km/h faster than the other train. While one train travels 70 km, the other travels 60 km. Find their speeds. A person traveled 120 miles in one direction. The return trip was accomplished at double the speed and took 3 hours less time. Find the speed going #1#1 #2#2 #3#3 #4#4 HomeworkHomework


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