The time taken by her if she works all alone.

BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 85RE
To determine

Expert Solution

Answer to Problem 85RE

She needs 6 hours to finish the painting alone.

Explanation of Solution

Given information:

It takes 60 minutes to pain a living room if all three work.

Calculation:

Let us suppose that:

x = the hours that Abbie needs to paint the living room alone

y = the hours that Beth needs to paint the living room alone

z = the hours that Cathie needs to paint the living room alone

t = 60 min = 1 hour the time they need to pain the room working all 3 together

Since she paints twice as fast as Beth

x=2y

Since she paints three times as fast as Cathie

x = 3z

if they pain together, they finish in 1 hour

1x + 1y + 1z = 1

by solving the system of 3 equations

x=2y

x = 3z

1x + 1y + 1z = 1

x = 6 hours

She needs 6 hours to finish the painting alone.

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