## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Practice and Problem-Solving Exercises - Page 376: 39

#### Answer

$2.75$ seconds

#### Work Step by Step

Firework A will fly for x seconds and reach a height of $220x$ feet Firework B will fly for y seconds and reach a height of $200y$ feet We are given $y=x+0.25\qquad$ ... B flies longer $220x=200y\qquad$ ... they reach the same height Substitute $x+0.25$ for $y$ in the second equation $220x=200(x+0.25)$ $220x=200x+50\quad$ ... add $-200x$ $20x=50$ $x=\displaystyle \frac{50}{20}=2.5$ Substitute $2.5$ for $x$ in $y=x+0.25$ $y=2.75$ Revert to the meanings of x and y: Firework A will fly for $2.5$ seconds and reach a height of $220(2.5)=550$ feet Firework B will fly for $2.75$ seconds and reach a height of $200(2.75)=550$ feet

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