# The speed of southbound boat.

### 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 74E
To determine

## To find: The speed of southbound boat.

Expert Solution

The speed of southbound boat is 9 mi/h.

### Explanation of Solution

Given:

The speed of eastbound boat is 3 mi/h faster than the speed of southbound boat.

The boats are 30 miles apart after 2 hour.

Formula used:

Distance formula is,

distance=time×rate

Calculation:

Let the speed of southbound boat be x.

Tabulate the given information into the language of algebra.

 Speed Time Distance Southbound x 2 2x Eastbound x+3 2 2(x+3)

Model the equation for the above information. Eastbound boat and southbound boat are travelling at right angles to each other.

(base)2+(height)2=(hypotenuse)2(2x)2+[2(x+3)]2=(30)2

Simplify the above equation for x,

4x2+4(x+3)2=9004x2+4(x2+9+6x)=9004x2+4x2+36+24x=9008x2+24x864=0

Factor the above equation.

x2+3x108=0(x9)(x+12)=0x=9,x=12

The speed cannot be negative, so the speed of southbound boat is 9 mi/h.

Thus, the speed of southbound boat is 9 mi/h.

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