/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 Marshall Dillon is riding at \(3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 3

Marshall Dillon is riding at \(30 \mathrm{mph}\) after the robber of the Dodge City bank, who has a head start of 15 minutes, but whose horse can only make \(25 \mathrm{mph}\) on a good day. How long does it take for Dillon to catch up with the bad guy, and how far from Dodge City are they when this happens? (Assume the road is straight, for simplicity.)

Short Answer

Expert verified
It takes Dillon 1.25 hours to catch the robber, and they will be 37.5 miles from Dodge City.

Step by step solution

01

Establish the Variables

Let the time it takes for Dillon to catch the robber be denoted as 饾憽 hours. The robber has a head start and thus starts with some initial distance. All speeds are in mi/hr.
02

Calculate the Robber鈥檚 Head Start

The robber's head start in time is 15 minutes, which is 0.25 hours. Given the robber's speed, the initial head start distance is: \( d_{\text{robber\text{head start}}} = 25 \text{ mph} \times 0.25 \text{ hours} = 6.25 \text{ miles} \)
03

Write Distance Equations

Construct the total distance each of them travels as functions of time. For the robber: \( d_{\text{robber}} = 25t + 6.25 \) miles For Dillon: \( d_{\text{Dillon}} = 30t \) miles
04

Set the Distances Equal

Dillon catches the robber when they have traveled the same distance, so set the two distance equations equal to each other and solve for 饾憽: \( 30t = 25t + 6.25 \)
05

Solve for Time

Isolate 饾憽 by subtracting 25饾憽 from both sides: \( 30t - 25t = 6.25 \) \( 5t = 6.25 \) \( t = \frac{6.25}{5} = 1.25 \) hours
06

Calculate the Distance from Dodge City

Using the time 饾憽 = 1.25 hours, substitute it back into Dillon鈥檚 distance equation: \( d_{\text{Dillon}} = 30 \times 1.25 = 37.5 \) miles Therefore, Dillon catches up with the robber 37.5 miles from Dodge City.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Problem-Solving in Physics
To solve physics problems effectively, it's crucial to follow a systematic approach. Here鈥檚 a step-by-step method using our example:

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You are trying to pass a truck on the highway. The truck is driving at \(55 \mathrm{mph}\), so you speed up to \(60 \mathrm{mph}\) and move over to the left lane. If the truck is \(17 \mathrm{~m}\) long, and your car is \(3 \mathrm{~m}\) long (a) how long does it take you to pass the truck completely? (b) How far (along the highway) have you traveled in that time? Note: to answer part (a) look at the problem from the perspective of the truck driver. How far are you going relative to him, and how far would it take you to cover \(20 \mathrm{~m}\) at that speed?
See all solutions

Recommended explanations on Physics Textbooks

Electrostatics

Read Explanation

Fundamentals of Physics

Read Explanation

Electricity and Magnetism

Read Explanation

Linear Momentum

Read Explanation

Fluids

Read Explanation

Fields in Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.