Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 6 - Systems of Equations and Inequalities - 6-4 Applications of Linear Systems - Got It? - Page 389: 2

Answer

The solution $(-2,14)$ is not a viable solution because it is not possible to have time be -2 hours. So, the tanks never have the same amount of water.

Work Step by Step

Let x = the number of hours the tanks are leaking and let y = the amount of water left in the tank. The first tank contains 10 gal of water and is leaking at a constant rate of 2 gal/h: $y=10-2x$ The second tank contains 6 gal of water and is leaking at a constant rate of 4 gal/h: $y=6-4x$ Using substitution to solve the equation: $6-4x=10-2x$ $2x=-4$ $x=-2$ Substitute -2 for x in either equation and solve for y. $y=10-2(-2)=14$ The solution $(-2,14)$ is not a viable solution because it is not possible to have time be -2 hours. So, the tanks never have the same amount of water.
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