Answer: The answer is: " 322.7 ft. "
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Step-by-step explanation:
First:
Convert: " 22 mi /h" ; to: " ft / s " ;
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Note the following exact conversions:
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1 mi = 5280 ft. ;
1 h = 60 min.
1 min = 60 s ;
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[tex]\frac{22 mi}{h} *\frac{5280ft}{mi} *\frac{1 h}{60 min}*\frac{1 min}{60 s}[/tex] = ? ft/sec. ?
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From the "left-hand side" of the equation:
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1) The units of "mi" ["mile(s}"] cancel out; since: "mi/mi" = 1 .
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2) The units of "h" ["hour(s)"] cancel out; since: "h/h" = 1 .
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3) The units of "min" ["minute(s)"] cancel out; since: "min/min" = 1.
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And we are with units of "ft/s" ["feet per second"] :
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→ " [tex](\frac{22*5280}{60*60}) \frac{ft}{s}[/tex] "; Using calculator:
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= " [tex](\frac{116160}{3600}) \frac{ft}{s}[/tex] " ; Using calculator:
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= " [tex]32.2666666667 \frac{ft}{sec}[/tex] " ;
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Now, we are asked:
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"How many feet will it cover in 30 seconds?"
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To solve:
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" [tex]\frac{32.2666666667 ft}{s} *\frac{10 s}{1 } = ? ft[/tex] " ;
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Note: The units of "s" ["second(s)"] on the "left-hand side" of the equation; cancel out to "1" ; since: "s/s" = 1 ;
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And we have:
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" ( [tex]32.2666666667 * 10[/tex] ) ft ;
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→ [tex]= 322.666666667[/tex] ft ;
{Note: To multiply by "10"; move the decimal one space to the right; or use calculator to get the value;
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Second:
→ We are asked to round our answer to the "nearest tenth of a foot" ;
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We have: " 322.666666.... ft." :
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Note: "322.666..."
The "tenths" place has a digit of "6".
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The question is: To round to the nearest tenth:
Do we round to "322.6" ? or round up to: "322.7" ?
To determine this, we examine the next following decimal; that is,
the "hundredths" place.
If the digit within the hundredths place is: "0, 1, 2, 3, or 4" ; then, we "round down" to "322.6 ".
If the digit within the hundredths place is: "5, 6, 7, 8, or 9" ; then, we "round up" to "322.7 ".
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In our case, the digit within the hundredths place is "6" ;
As such, we round to: "322.7" .
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The answer is: " 322.7 ft. "
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Hope this answer—and explanation—is helpful to you!
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