Question 175478
Let t=time and r=rate/speed


"The amount of time for a trip varies inversely as the speed traveled" translates to {{{t=k/r}}}



Now find the value of k:



{{{t=k/r}}} Start with the given equation.



{{{9=k/60}}} Plug in {{{t=9}}} and {{{r=60}}}



{{{9*60=k}}} Multiply both sides by 60 to isolate k.



{{{540=k}}} Multiply



So the value of k is {{{k=540}}}



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So the equation becomes {{t=540/r}}} after plugging in {{{k=540}}}



Now let's answer the question: "What must its speed be to get there in only 8 hours?"


{{{t=540/r}}} Start with the given equation.



{{{8=540/r}}} Plug in {{{t=8}}}



{{{8r=540}}} Multiply both sides by r.



{{{r=(540)/(8)}}} Divide both sides by {{{8}}} to isolate {{{r}}}.



{{{r=135/2}}} Reduce.



{{{r=67.5}}} Divide.



So the speed would need to be 67.5 mph in order to get there in 8 hrs