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 64E
To determine

To find: The time taken by Bob hose and Jim hose to fill the pool.

Expert Solution

Answer to Problem 64E

The time taken by Bob hose is 32.4 hours and time taken by Jim hose is 40.5 hours.

Explanation of Solution

Given:

They both take 18 hours to fill the pool.

Bob’s hose takes 20% less time than Jim’s hose alone.

Calculation:

Let the time taken by Jim’s hose be x.

Time taken by Bob’s hose,

Time=x20%ofx=x0.20x=0.80x

Tabulate the given information into the language of algebra.

In words In Algebra
Time taken by Jim’s x hr
Time taken by Bob’s 0.80x hr
Work done by Jim’s hose 1x
Work done by Bob’s hose 10.80x
Work done by both hoses 118

Model the equation for the above information.

(FractiondonebyBob'shose)+(FractiondonebyJim'shose)=Fractiondonebyboth1x+10.80x=118

Simplify the above equation for x,

0.80+1=0.80x18(MultiplybyLCD0.80x)1.80=0.80x180.80x=32.4x=40.5

The taken by Jim’s hose is 4.05 hours.

Time taken by Bob’s hose,

0.80x=0.80×4.05=32.4

The time taken by Bob’s hose is 32.4 hours.

Thus, the time taken by Bob hose is 32.4 hours and time taken by Jim hose is 40.5 hours.

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