# The range of speed for which the vehicle has stopping distance that do not exceed 240ft. ### 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 1.7, Problem 117E
To determine

## The range of speed for which the vehicle has stopping distance that do not exceed 240ft.

Expert Solution

The range of speed is between 0 mi/h and 60 mi/h_.

### Explanation of Solution

The formula for distance to stop the car is d=v+v220 with the stopping distance 240ft or less, where d is the distance measured in feet (ft) and v is the speed of the car measured in mi/h.

Substitute the value of 240ft for d in d=v+v220 and calculate the value of v as follows.

Since the stopping distance is 240ft or less, the formula d=v+v220 will become 240v+v220. That is,

240v+v220v+v2202400v2+20v48000

On further simplification,

v2+20v48000v2+(8060)v48000v2+80v60v48000

Further solve the equation as follows.

v(v+80)60(v+80)0(v+80)(v60)0

Thus, v80 and v60.

Since the speed cannot be negative, 0v60.

Therefore, the range of speed is between 0 mi/h and 60 mi/h_.

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