objective: solve word problems involving uniform motion motion in opposite directions
TRANSCRIPT
OBJECTIVE: SOLVE WORD
PROBLEMS INVOLVING UNIFORM MOTION
Motion in Opposite Directions
Uniform Motion
Moving at a speed that is not changing.
Distance = Rate x Time
D = RT (dirt)Rate x Time = Distance
50mph x 2hours = 100miles
D/T = RDistance / Time = Rate
100miles / 2hours = 50mph
Distance = Rate x Time
D/R = TDistance /Rate = Time
100miles / 50mph = 2hours
Solving Word Problems
1. Draw a sketch 2. Identify Unknowns3. Assign Variable4. Make a Chart5. Write and solve an equation
Equation for Motion in Opposite Directions
Add distance for both objects and set equal to the total distance apart.
Example Bike riders Brent and Jane started at noon from points 60 km apart and rode toward each other, meeting at 1:30pm. Brent’s speed was 4km/h greater than Jane’s speed.
Find their speeds.
Start riding at 12pm & meet at 1:30pm
Unknown
Jane and Brent’s speed.
Variables
Let r = Jane’s rateLet r + 4 = Brent rate
Make a chart and use the information to label your diagram
Chart
BIKE RIDINGBIKE RIDING RATERATE TIMETIME DISTANCEDISTANCE
JANEJANE
BRENTBRENT
Equation
1.5 ( r + 4) + 1.5r = 60r = 18 Jane’s speedr + 4 = 22 Brent’s speed
Brent’s speed was 22km/h and Jane’s speed was 18 km/h
Try ThisAt noon a private plane left Austin for Los Angeles, 2100km away, flying at 500 km/h. One hour later a jet left Los Angeles for Austin at 700km/h. At what time did they pass each other?
2100 km
500 km
700 km
500t + 700(t – 1) = 2100
TRAVELTRAVEL RATERATE TIMETIME DISTANCEDISTANCE
PLANEPLANE
JETJET
500
700
t
1t
500t
700( 1)t
500t + 700(t – 1) = 2100
500t +700t – 700 = 2100
1200t – 700 = 2100
+700 =+700
1200t = 2800
1200t/1200 =2800/1200
T=2 and 400/1200 HRS or 2 and 1/3hrs is 2hrs 20min
WHATS THE QUESTION Airplane took 2 hours and 20 min before meeting with
Jet that took t – 1 =2hr 20 min – 1 = 1hr and 20 min
Time is 12:00 + 2 hr and 20 min . They jet passed the plane at 2:20