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 19P
To determine

To find: the rate of the boat in still water.

Expert Solution & Answer
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Answer to Problem 19P

The rate of boat in still water is 15km/h .

Explanation of Solution

Given:

A motorboat goes 36 km downstream and 24 km upstream in the same amount of time.

Concept used:

Speed and the rate have same meaning here.

  Distance=rate×time .

In the elimination method:

Either add or subtract equation to get an equation in one variable.

When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.

Calculation:

Let r be the rate in still water and t be the time takes for both directions.

If the current is 3km/h ,then the rate downstream is r+3 and the rate upstream is r-3 .

Using formula:

  distance=rate×time :

  36=(r+3)t .

Dividing both side by r+3 :

  t=36r+3 ………………. (i)

Similarly,

  24=(r-3)t .

Dividing both side by r-3 :

  t=24r-3 ……………….. (ii)

Equating the equation (i) and (ii) :

  36r+3=24r-3 .

  36(r-3)=24(r+3) .

  24r+72=36r-108 .

  r=15 .

Hence, the rate of boat in still water is 15km/h .

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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