When the wind is blowing at 25 mph, a plane flying at a constant speed can travel 500 mi with th

Name: Problem 24, Chapter 8: Beginning and Intermediate Algebra
Uploaded: 2020-06-28T22:19:57-08:00
Duration: 1 min 53 s
Channel: Liuxi Sun
Description: When the wind is blowing at 25 mph, a plane flying at a constant speed can travel 500 mi with the wind in the same amount of time it can fly 400 mi against the wind. Find the speed of the plane.

step 1 scenario, an airplane is traveling X miles per hour, and the wind is traveling at 25 miles per h

Question

When the wind is blowing at $25 \mathrm{mph}$, a plane flying at a constant speed can travel 500 mi with the wind in the same amount of time it can fly 400 mi against the wind. Find the speed of the plane.

   When the wind is blowing at $25 \mathrm{mph}$, a plane flying at a constant speed can travel 500 mi with the wind in the same amount of time it can fly 400 mi against the wind. Find the speed of the plane.

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 8, Problem 24

Instant Answer

Solved by Expert Liuxi Sun

06/28/2020

Step 1

In this case, the time it takes to travel 500 miles with the wind is equal to the time it takes to travel 400 miles against the wind. We can write this as: $$\frac{500}{x+25} = \frac{400}{x-25}$$ Show more…

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When the wind is blowing at $25 \mathrm{mph}$, a plane flying at a constant speed can travel 500 mi with the wind in the same amount of time it can fly 400 mi against the wind. Find the speed of the plane.

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Key Concepts

Relative Velocity

This concept deals with how the effective speed of an object is altered by external factors. Here, the plane’s speed relative to the ground is the sum of its airspeed and the wind speed when flying with the wind, and the difference when flying against it.

Distance-Speed-Time Relationship

This principle states that time equals distance divided by speed. It is fundamental for modeling motion, as it allows one to calculate travel time when distance and speed are known.

Setting Up Equations

By recognizing that the travel times for the two different scenarios are equal, one can set up an equation directly linking the two time expressions. This forms the basis for solving for the unknown airspeed.

Solving Linear Equations

Once the equation is established, standard algebraic techniques for solving linear equations are applied to isolate and calculate the desired variable—in this case, the plane's speed relative to the air.

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