Mathematics

Grade Levels: 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade,

Topics: AlgebraExpressions and Equations

Common Core State Standard: A-CED.2, A-CED.4,

Knowledge and Skills:

· Can evaluate expressions by substituting values for variables

· Can simplify expressions using correct order of operations

· Can do basic operations on both sides of an equation in such a way as to preserve the equality

Lesson:

**Response Time**

If you send a signal over a fiber optic cable to another computer and get a response, the response time, t_{response}, depends on three things:

a) the distance between you and the computer, L

b) the velocity of light traveling through the cable, v

c) the amount of time it takes the other computer to process your signal, t_{processing }

The equation you would use to find the response time is this:

Note that the velocity of light in fiber optic cable, v, is about 2/3 of the velocity of light in a vacuum, which makes it approximately equal to 200,000,000 meters/second.

1. Calculate t_{response} for the given values of L and t_{processing}:

L |
t_{processing} |
t_{response} |

500,000 meters | 0.013 seconds | |

8,000,000 meters | 0.005 seconds | |

2,000 meters | 0.002 seconds | |

20,000,000 meters | 0.04 seconds |

2. Solve the equation to find the unknown value:

L |
t_{processing} |
t_{response} |

750,000 | ? | 0.0325 |

? | 0.001 | 0.00195 |

? | 0.015 | 0.016 |

50,000,000 | ? | 0.503 |