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Dafna11 [192]
3 years ago
8

One tank is filling at a rate of 5/8 gallon per 7/10 hour. A second tank is filling at a rate of 5/9 gallon per 2/3 hour. Which

tank is filling faster? Explain how you know.
Mathematics
1 answer:
anzhelika [568]3 years ago
3 0
First recognize that the unit rate we're finding is gallons per hour, or \frac{g}{h}.

rate for Tank 1 = x gallons per hour = <em>a</em> gallons / <em>b</em> hours

T_{1}=\frac{\frac{5}{8}}{\frac{7}{10}}\\\\T_{1}=\frac{5}{8}*\frac{10}{7}\\\\T_{1}=\frac{50}{56}\\\\\\Fill\ rate\ of\ Tank\ 1=\frac{25}{28}


rate for Tank 2 = y gallons per hour = <em>c</em> gallons / <em>d</em> hours

T_{2}=\frac{\frac{5}{9}}{\frac{2}{3}}\\\\T_{2}=\frac{5}{9}*\frac{3}{2}\\\\T_{2}=\frac{15}{18}\\\\T_{2}=\frac{15}{18}\\\\\\Fill\ rate\ of\ Tank\ 2=\frac{5}{6}
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Andre45 [30]

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The first statement in the biconditional is An integer is divisible by 100 if its last two digits are zeros.  The converse of this would be An integer's last two digits are zeros if it is divisible by 100.  Joining these using "if and only if" creates our biconditional.

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