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 1.6, Problem 66E
To determine

To find: The time taken by Kay to all the flyers alone.

Expert Solution

Answer to Problem 66E

Kay takes 3 hours to deliver all the flyers.

Explanation of Solution

Given:

Jack takes 4 hours to deliver all the flyers. Lynn takes 1 hour longer than Kay.

They work together and deliver all the flyers in 40% of the time takes by Kay.

Calculation:

Let the time taken by Kay to deliver the flyers be x.

Tabulate the given information into the language of algebra.

In words In Algebra
Time taken by Kay x hr
Time taken by Lynn (x+1) hr
Time taken by all of them 0.4x hr
Work done by Kay in 1 hr 1x
Work done by Lynn in 1 hr 1x+1
Work done by Jack in 1 hr 14
Work done by Jack, Kay and Lynn together 10.4x

Model the equation for the above information.

(FractiondonebyJack)+(FractiondonebyKay)+(FractiondonebyLynn)=Fractiondonetogether14+1x+1x+1=10.4x

Simplify the above equation for x,

x(x+1)+4(x+1)+4x=4x(x+1)0.4x(MultiplybyLCD4x(x+1))x2+x+4x+4+4x=10(x+1)x2+9x+4=10x+10x2x6=0

Factor the above equation for x,

(x3)(x+2)=0x=3,x=2

Time cannot be negative. So Kay takes 3 hours to complete the work.

Thus, Kay takes 3 hours to deliver all the flyers.

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