# Chapter 9 - Section 9.4 - Applications Involving Pairs of Linear Equations - Exercises - Page 338: 3

The 180 gal/h pump was operated for 2.5 hours. The 250 gal/h pump was operated for 3.5 hours.

#### Work Step by Step

Let x be the time in operation of the 180 gal/h pump and y be the time in operation of the 250 gal/h pump. $x+y=6$ since the total test time was 6 hours. $180x+250y=1325$ since the total amount pumped was 1325 gal. Multiply both sides of the first equation by -250, then add the two equations. $-250x-250y=-1500$ $\underline{\ \ \ 180x+250y=\ \ \ 1325}$ $\ -70x\ \ \ \ \ \ \ \ \ \ \ \ =-175$ $\longrightarrow$ divide both sides by -70 to solve for x $-70x\div-70=-175\div-70$ $x=2.5$ Substitute 2.5 for x in the first equation to solve for y. $2.5+y=6$ $2.5+y-2.5=6-2.5$ $y=3.5$

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