Question

A work crew has a new pump and an old pump. The new pump can fill a tank in 5 hours, and the old pump can fill the same tank in 7 hours. Write and solve an equation for the time it will take both pumps to fill one tank if the pumps are used together

Answer 1

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new pump rate:: $\frac{1}{5}$ job/hr
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old pump rate:: $\frac{1}{7}$ job/hr
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together rate:: $\frac{1}{x}$ job/hr
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Equation:
rate + rate = together rate
$\frac{1}{5}$ + $\frac{1}{7}$ = $\frac{1}{x}$7x + 5x = 35
12x = 35
x = $\frac{35}{12}$ = 2 $\frac{11}{12}$ hr = 2hr 55 min (time to do the job together)