Question

Comparing Travel. A bicyclist can travel 40 miles in the same time that a motorcyclist can travel 60 miles. If the bicyclist travels 12 mph slower than the motorcyclist, find the speed of the motorcyclist.

Name: Problem 38, Chapter 6: Intermediate Algebra
Uploaded: 2020-08-08T15:17:38-08:00
Duration: 1 min 17 s
Channel: Kelsey Dondelinger
Description: Comparing Travel. A bicyclist can travel 40 miles in the same time that a motorcyclist can travel 60 miles. If the bicyclist travels 12 mph slower than the motorcyclist, find the speed of the motorcyclist.

   Comparing Travel. A bicyclist can travel 40 miles in the same time that a motorcyclist can travel 60 miles. If the bicyclist travels 12 mph slower than the motorcyclist, find the speed of the motorcyclist.

Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 6, Problem 38

Instant Answer

Solved by Expert Kelsey Dondelinger

08/08/2020

Step 1

We also know that time is equal to distance divided by speed. Therefore, we can set up the equation as follows: \[\frac{40}{x} = \frac{60}{x+12}\] Show more…

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Comparing Travel. A bicyclist can travel 40 miles in the same time that a motorcyclist can travel 60 miles. If the bicyclist travels 12 mph slower than the motorcyclist, find the speed of the motorcyclist.

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Key Concepts

Equating Time for Different Entities

When two objects or individuals complete different distances in the same amount of time, their time expressions (calculated as distance divided by speed) can be set equal to each other. This is a key technique for establishing a relationship between their speeds.

Setting Up and Solving Systems of Equations

In problems where multiple relationships are provided, such as differences in speed or distance, a system of equations can be formulated. Solving the system enables you to find the values of unknown variables, such as speed, through algebraic manipulation.

Rate, Distance, and Time Relationship

This fundamental concept in algebra and physics states that distance equals rate multiplied by time. It provides a way to relate how far an object travels with its speed and the time taken, and is commonly used to solve problems in uniform motion.

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