Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.8, Problem 19P

To determine

Find the time after which the private jet is twice as far from Dallas as the commercial jet.

Expert Solution & Answer

Answer to Problem 19P

2 hours 37.5 minutes

Explanation of Solution

Given :

A commercial jet can fly from San Francisco to Dallas in 3 h. A private jet can make the same trip in 312h. The two planes leave San Francisco at noon.

Calculation:

Let the distance between San Francisco and Dallas = d

Time taken by commercial jet to cover the distance = 3 h

Time taken by private jet to cover the distance = 312=72h

So,

speed of each plane:

vc=distancetime=d3

vp=distancetime=d7/2=2d7

Let the time after which the private jet is twice as far from Dallas as the commercial jet = t

So, we can find the distance of each plane from Dallas :

Distance of commercial plane from Dallas = dc=d−d3t.................[distance=speed×time]

Distance of private jet from Dallas = dp=d−2d7t.................[distance=speed×time]

Given ,

dp=2dc

Substitute the values of each and solve for t :

dp=2dc⇒d−2d7t=2(d−d3t)⇒d−2d7t=2d−2d3t⇒8d21t=d.................[subtract (d−2d3t) from each side]⇒t=218..................[divide each side by 218d]⇒t=258 hours⇒t=2 hours 58×60 minutes⇒t=2 hours 37.5 minutes

So, the time after which the private jet is twice as far from Dallas as the commercial jet is 2 hours 37.5 minutes.

Chapter 5.8, Problem 18P

Chapter 5.8, Problem 20P

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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