# The distance covered on the boardwalk. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.6, Problem 84E
To determine

## To find: The distance covered on the boardwalk.

Expert Solution

The distance covered on the boardwalk is 720 ft.

### Explanation of Solution

Given:

Distance between boardwalk and shoreline is 210 ft. Distance between man and umbrella is 750 ft.

The man walks 4 ft/s on boardwalk and 2 ft/s on the sand.

Time taken to reach the umbrella is exactly 4 min 45 sec.

Calculation:

Let the distance covered on the boardwalk be x.

Time taken to reach the umbrella in sec is,

4min45sec=(4×60+45)sec=(240+45)sec=285sec

Tabulate the given information algebraically.

 In words In algebra Length of boardwalk x

Model the equation for the above information.

(Distanceofmanfromumbrella)2=(Distancecoveronboardwalk)2+(Distanceofboardwalkfromumbrella)2(750)2=(x)2+(210)2

On further simplification,

562500=x2+44100x2=518400x=720

The distance covered on board walk is 720 ft.

Time taken to walk through the board-walk to a point directly in front umbrella is,

totaltime=timeonboardwalk+timeonsand=7204+2102=180+105=285sec

Thus, the distance cover on the boardwalk is 720 ft.

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