Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Chapter 9.6, Problem 4OE
To determine

Tofind:the rate of plane with wind and against wind.

Expert Solution & Answer
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Answer to Problem 4OE

The rate of the plane with the wind is p+w and the rate of the plane against wind is p-w .

Explanation of Solution

Given:

  Algebra: Structure And Method, Book 1, Chapter 9.6, Problem 4OE

Concept used:

If the plane is with the wind then it’s taken as +ive.

If the plane is against the windthen it’s taken as -ive .

Vector formula:

  R2=A2+B2+2ABcosθ .

If the direction of plane is with the wind means planemakes 00 with the wind.

The resultant will be:

  R2=A2+B2+2ABcos00 .

  R2=(A+B)2 .

  R=(A+B) .

Similarly,

If the direction of plane isagainst the wind means plane make 1800 with the wind.

  R2=A2+B2-2AB .

  R=A-B .

  distance=rate×time .

Calculation:

If the rate of the plane in still air is 700 and the rate of the wind is 50 ,then

1.The rate of the plane with the wind is:

  700+50=750 .

The rate of the plane against wind is:

  70050=650 .

If the rate of the plane in still air is 825 and the rate of the wind is 100 ,then

2.The rate of the plane with the wind is:

  825+100=925 .

The rate of the plane against wind is:

  825100=725 .

If the rate of the plane in still air is 900 and the rate of the wind is w ,then

3.The rate of the plane with the wind is:

  900+w .

The rate of the plane against wind is:

  900-w .

If the rate of the plane in still air is p and the rate of the wind is w ,then

3.The rate of the plane with the wind is:

  p+w .

The rate of the plane against wind is:

  p-w .

Hence the table is

    Rate of plane in still airRate of windRate of plane with windRate of plane against the wind
    70050750650
    825100925725
    900w900+w900-w
    pwp+wp-w

Hence, the rate of the plane with the wind is p+w and the rate of the plane against wind is p-w .

Chapter 9 Solutions

Algebra: Structure And Method, Book 1

Ch. 9.1 - Prob. 2WECh. 9.1 - Prob. 3WECh. 9.1 - Prob. 4WECh. 9.1 - Prob. 5WECh. 9.1 - Prob. 6WECh. 9.1 - Prob. 7WECh. 9.1 - Prob. 8WECh. 9.1 - Prob. 9WECh. 9.1 - Prob. 10WECh. 9.1 - Prob. 11WECh. 9.1 - Prob. 12WECh. 9.1 - Prob. 13WECh. 9.1 - Prob. 14WECh. 9.1 - Prob. 15WECh. 9.1 - Prob. 16WECh. 9.1 - Prob. 17WECh. 9.1 - Prob. 18WECh. 9.1 - Prob. 19WECh. 9.1 - Prob. 20WECh. 9.1 - Prob. 21WECh. 9.1 - Prob. 22WECh. 9.1 - Prob. 23WECh. 9.1 - Prob. 24WECh. 9.1 - Prob. 1MRECh. 9.1 - Prob. 2MRECh. 9.1 - Prob. 3MRECh. 9.1 - Prob. 4MRECh. 9.1 - Prob. 5MRECh. 9.1 - Prob. 6MRECh. 9.1 - Prob. 1CECh. 9.1 - Prob. 2CECh. 9.1 - Prob. 3CECh. 9.1 - Prob. 4CECh. 9.2 - Prob. 1OECh. 9.2 - Prob. 2OECh. 9.2 - Prob. 3OECh. 9.2 - Prob. 4OECh. 9.2 - Prob. 5OECh. 9.2 - Prob. 6OECh. 9.2 - Prob. 7OECh. 9.2 - Prob. 8OECh. 9.2 - Prob. 9OECh. 9.2 - Prob. 10OECh. 9.2 - Prob. 11OECh. 9.2 - Prob. 12OECh. 9.2 - Prob. 1WECh. 9.2 - Prob. 2WECh. 9.2 - Prob. 3WECh. 9.2 - Prob. 4WECh. 9.2 - Prob. 5WECh. 9.2 - Prob. 6WECh. 9.2 - 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