Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.9, Problem 19P

To determine

To find how long would it take pipe C to empty it

Expert Solution & Answer

Answer to Problem 19P

The total time taken by pipe C to empty the tank be 5 hr

Explanation of Solution

Given that

Work done by pipe A in one hour be 15

Now , Work done by pipe A in 3 hour to fill the tank be 35 ......................(i)

Let work done by pipe C in one hour be 1x

Now , work done by pipe C in 3 hour to drain the tank be 3x..................(ii)

Similarly

Let work done by pipe B in one hour which is less than 2 hr of pipe C be 1x−2

Now , work done by pipe C in 3 hour to fill the tank be 3x−2..................(iii)

Consider the sum of the work done by all three pipes A, B and C will be 1

Add equation (i) , (ii) because both A and B filled the tank whereas subtract from (iii) because it drained from the tank C and compare with 1

35+3x−2−3x=13(x−2)(x)+3(x)(5)−3(5)(x−2)=5x(x−2)3x2−6x+15x−15x+30=5x2−10x2x2−4x−30=0x2−2x−15=0x2−(5−3)x−15=0x(x−5)+3(x−5)=0(x−5)(x+3)=0x=5,−3

Therefore, time will not be equal to negative, So , 5 hr will be the total time taken by C to empty the tank.

Hence, The total time taken by pipe C to empty the tank be 5 hr

Chapter 5.9, Problem 18P

Chapter 5.9, Problem 20P

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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