Solving Systems of Equations

1
Solving Systems of Equations

• Classic Applications (Travel)

2
Objectives

• Define the variables in Travel application
  problems.
• Use the variables to set up the system of
  equations.
• Solve the system using the Elmination or
  Substitution Methods.

3
Travel Problems.
A plane leaves New York City and heads for
Chicago, which is 750 miles away. The plane,
flying against the wind, takes 2.5 hours to reach
Chicago. After refueling the plane returns to New
York, traveling with the wind, in 2 hours. Find
the rate of the wind and the rate of the plane
with no wind.
rate of the plane without any wind
x
y
the rate of the wind
4
Travel Problems.
x
rate of the plane without any wind
y
the rate of the wind
Two Scenarios
Rate against the wind NYC to Chicago
x - y
Time
2.5 hours
Distance 750mi
x y
Time
2 hours
Distance 750mi
Rate with the wind Chicago to NYC
Distance Rate x Time
5
Travel Problems.
x
rate of the plane without any wind
y
the rate of the wind
Two Scenarios
Rate x Time Distance
(x - y)
2.5

750 miles
NYC to Chicago
(x y)
2.0

750 miles
Chicago to NYC
Distance Rate x Time
6
Travel Problems.
A boat can travel 10 miles downstream in 2 hours
and the same distance upstream in 3.5 hours. Find
the rate of the boat in still water and the rate
of the current.
x
rate of the boat in still water
y
the rate of the wind
7
Travel Problems.
x
rate of the boat in still water
y
rate of the current
Two Scenarios
Rate of the boat going downstream
x y
Time
2 hours
Distance 10mi
x - y
Time
3.5 hours
Distance 10mi
Rate of the boat Going upstream
Distance Rate x Time
8
Travel Problems.
x
rate of the boat in still water
y
rate of the current
Two Scenarios
Rate x Time Distance
Downstream
(x y)
2

10 miles
Upstream
(x - y)
3.5

10 miles
Distance Rate x Time