9th Edition

ISBN: 9780321716835

Author: Michael Sullivan

Publisher: Addison Wesley

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Question

Chapter 11, Problem 107RE

To determine

How long will it take each of them working alone to finish the job?

Expert Solution & Answer

Answer to Problem 107RE

$4,2and8$ hours respectively.

Explanation of Solution

Given information:

If Bruce and Bryce work together for $1$ hour and $20$ minutes, they will finish a certain job. If Bryce and Marty work together for $1$ hour and $36$ minutes, the same job can be finished. If Marty and Bruce work together, they can complete this job in $2$ hours and $40$ minutes. How long will it take each of them working alone to finish the job?

Calculation:

Let $x$ denote the work of Bruce, $y$ denote the work of Bryce and $z$ denote that of Marty.

The total time taken, in minutes, by Bruce and Bryce to finish the job is $80$ . So, the work done will be $1x+1y=180$ .

The total time taken, in minutes, by Bryce and Marty to finish the job is $96$ . So, the work done will be $1y+1z=196$ .

The total time taken, in minutes, by Marty and Bruce to finish the job is $160$ . So, the work done will be $1x+1z=1160$ .

A system of three equations is formed.

${1x+1y=1801y+1z=1961x+1z=1160$

Subtract the second equation from the first to eliminate $1y$ .

$1x+1y−(1y+1z)=180−196$

$1x−1z=96−807680$

$=167680$

$=1480$

Add the above equation to the third equation in the system.

$1x−1z+1x+1z=1480+1160$

$2x=160+480480.160$

$=64076800$

Simplify the expression to find $x$ .

$2.76800=x.640$

$153600=640x$

$x=153600640$

$=240$

Divide by $60$ to find the time taken in hours.

$x=24060$

$=4$

Substitute $240$ for $x$ in the first equation in the system to find $y$ .

$1240+1y=180$

$1y=180−1240$

$=2240$

Take the reciprocal to find $y$ .

$y=2402$

$=120$

Divide by $60$ to find the time taken in hours.

$y=12060$

$=2$

Substitute $120$ for $y$ in the second equation in the system to find $z$ .

$1120+1z=196$

$1z=196−1120$

$=5−4480$

$=1480$

Take the reciprocal to find $y$ .

$z=480$

Divide by $60$ to find the time in hours.

$z=48060$

$=8$

Hence, the times taken by Bruce, Bryce, and Marty to finish the job alone are $4,2and8$ hours respectively.

Chapter 11, Problem 106RE

Chapter 11, Problem 108RE

Chapter 11 Solutions

Precalculus

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