1110B Distance Motion Problems Part II

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11-10B Distance (Motion) Problems Part II
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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Yesterday you studied motion problems of the
type
Sometimes, problems about motion involve two
people traveling the same distance. In such
cases, you can write an equation by setting the
algebraic representations for these distances
equal to each other.
In this type of problem, the total distance is
unknown.
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Sam started out in his car traveling at 60 km/h.
Two hours later, Jenny left from the same point.
She drove the same road at 75 km/h. How many
hours had she driven before she caught up with
Sam?
point where Jenny caught up with Sam
start
Sam
Jenny
It may be helpful to draw a sketch.
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Sam started out in his car traveling at 60 km/h.
Two hours later, Jenny left from the same point.
She drove the same road at 75 km/h. How many
hours had she driven before she caught up with
Sam?
let t Jennys time
Assign Labels.
let t 2 Sams time
Verbal Model.
Sams distance Jennys distance
Algebraic Model.

Substitute rt for d
Substitute given values.
Solve.
Sentence.
It took Jenny 8 hours to catch up to Sam.
The problem gives the rate. You are asked to
find the time. Whose time do you need to find?
You do not know distance, but you do know that
drt so substitute!
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Example 1 A train left a station traveling 100
km/h. A second train left 2 hours later and
headed in the same direction at 125 km/h. After
how many hours did the second train overtake the
first?
point where trains meet.
start
1st train
2nd train
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Example 1 A train left a station traveling 100
km/h. A second train left 2 hours later and
headed in the same direction at 125 km/h. After
how many hours did the second train overtake the
first?
Assign Labels.
let t 2nd trains time
let t 2 1st trains time
1st trains distance 2nd trains distance
Which trains time do you need to find?

The second train overtook the first train in 8
hours.
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Example 2 The Peterson family drove to the beach
at 75 km/h. They returned later in heavy
traffic, at 50 km/h. It took 1 hour longer to
return home than it did to get to the beach. How
long did it take to get home?
to the beach
return home
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Example 2 The Peterson family drove to the beach
at 75 km/h. They returned later in heavy
traffic, at 50 km/h. It took 1 hour longer to
return home than it did to get to the beach. How
long did it take to get home?
Assign Labels.
let t time to get home
let t 1 time to beach
distance to beach distance to return home

Which time do you need to find?
It took the Peterson family 3 hours to return
home.
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Example 3 A plane flew from Los Angles to
Minneapolis at 800 km per hour and then returned
to Los Angeles at 900 km per hour. The return
trip took 30 minutes less than the flight to
Minneapolis. How long did the trip to
Minneapolis take?
Los Angeles
Minneapolis
to Minneapolis
back to Los Angeles
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Example 3 A plane flew from Los Angles to
Minneapolis at 800 km per hour and then returned
to Los Angeles at 900 km per hour. The return
trip took 30 minutes less than the flight to
Minneapolis. How long did the trip to
Minneapolis take?
Assign Labels.
let t time to Minn.
let t 0.5 time to L.A.
distance to Minn. distance to Los Angeles
Which time do you need to find?

It took 4.5 hours to fly from LA to Minneapolis.
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• Practice Problems
• The Olsen family drove to the mountains at 60
  km/h. On the trip home they drove 40 km/h. The
  return trip took 2 hours longer than the trip to
  the mountains. How long did it take them to get
  home?
• Tina started out in her car at the rate of 50
  km/h. One hour later, Alex left from the same
  point driving along the same road at 75 km/h.
  How long did it take Alex to catch up with Tina?
• The Brown family drove to their parents house at
  45 km/h. The return trip took 1 hour less
  because they traveled at 60 km/h. How long did
  it take them to get home?

• It took 6 hours for the Olsen family to return
  home.
• Alex caught up with Tina after two hours.
• It took 3 hours for the Brown family to return
  home.

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Homework
11-A11 Handout A11
Algebra Rocks!