Question

In Exercises $53-62,$ some applications of inequalities are shown. A driver using the Google Maps app finds that it is 300 mi to her destination. If her speed always stays between $50 \mathrm{mi} / \mathrm{h}$ and $60 \mathrm{mi} / \mathrm{h}$ use an inequality to express the required time $t$ for the trip.

Name: Problem 61, Chapter 17: Basic Technical Mathematics with Calculus
Uploaded: 2021-06-25T15:30:53-08:00
Duration: 1 min 57 s
Channel: Audrey Fong
Description: In Exercises 53-62, some applications of inequalities are shown. A driver using the Google Maps app finds that it is 300 mi to her destination. If her speed always stays between 50 mi / h and 60 mi / h use an inequality to express the required time t for the trip.

   In Exercises $53-62,$ some applications of inequalities are shown.
A driver using the Google Maps app finds that it is 300 mi to her destination. If her speed always stays between $50 \mathrm{mi} / \mathrm{h}$ and $60 \mathrm{mi} / \mathrm{h}$ use an inequality to express the required time $t$ for the trip.

Basic Technical Mathematics with Calculus

Allyn J. Washington,… 11th Edition

Chapter 17, Problem 61

Instant Answer

Solved by Expert Audrey Fong

06/25/2021

Step 1

Time t = 300/v, so taking reciprocals gives 1/60 ≤ 1/v ≤ 1/50. Show more…

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In Exercises $53-62,$ some applications of inequalities are shown. A driver using the Google Maps app finds that it is 300 mi to her destination. If her speed always stays between $50 \mathrm{mi} / \mathrm{h}$ and $60 \mathrm{mi} / \mathrm{h}$ use an inequality to express the required time $t$ for the trip.

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Key Concepts

Distance-Rate-Time Relationship

This fundamental concept in algebra relates the distance traveled to the rate (or speed) and the time of travel. It is typically expressed by the formula distance = speed * time, which can be rearranged to find the time as time = distance/speed. This relationship is crucial for solving problems that involve motion at constant speeds.

Inequalities and Variable Constraints

In many real-world scenarios, certain variables have bounds rather than being fixed values. When a variable, such as speed, is known to be between a lower and an upper limit, inequalities are used to represent these constraints. Applying the distance-rate-time relationship within these bounds allows us to create an inequality that represents the possible values for time based on the changing speed.

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