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Solving Systems of Equations. Classic Applications (Travel). 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. Travel Problems.

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Solving Systems of Equations

Classic Applications (Travel)


Objectives l.jpg
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.


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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


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Travel Problems.

= rate of the plane without any wind

x

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


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Travel Problems.

= rate of the plane without any wind

x

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


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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.

= rate of the boat in still water

x

y

= the rate of the wind


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Travel Problems.

= rate of the boat in still water

x

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


Travel problems8 l.jpg
Travel Problems.

= rate of the boat in still water

x

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


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